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1
Tilumanywa, Verdiana T. "Land use and livelihood changes in the Mount Rungwe ecosystem, Tanzania." Thesis, Stellenbosch : Stellenbosch University, 2013. http://hdl.handle.net/10019.1/85786.
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Thesis (PhD)--Stellenbosch University, 2013.<br>ENGLISH ABSTRACT: The Mount Rungwe ecosystem (MRE) has unique mountain resources. Its biological, hydrological, economic and cultural endowments offer many development opportunities for Tanzania. Since the 1970s, the MRE has experienced change in land use and means of acquiring livelihoods, calling for scientific investigation into the extent, nature, and magnitude of land use changes and their implications for communities’ livelihoods.
The aim of the study was to investigate the major changes in land use, to identify the drivers responsible for these changes and to establish the interrelationship between land use change and communities’ livelihoods in order to suggest desirable management options towards improving rural livelihoods and the ecological integrity of MRE. A research design that integrates both qualitative and quantitative approaches was adopted. The fieldwork involved six villages representative of three ecological zones and 384 respondents were interviewed. Information on the past and present land uses, policies, institutions and processes that have influenced and are influencing land use change in the area was obtained through questionnaires, interviews, field observation, and analysis of documents. Satellite imagery of 1973, 1986, 1991 and 2010 were analysed for spatial and temporal statistics on land use and change.
The findings indicate that MRE is experiencing land conversions from one land use category to the other especially in villages of the highland zone. Government policies on the use of and access to forests, agricultural land and energy have contributed to the past and current land use changes. Demographic, cultural, economic and natural factors singly or cumulatively have also induced changes in land use in MRE. Most of the changes in land use were noted between 1991 and 2010. At the district level there was a significant decrease in natural vegetation, particularly bushland and woodland, and an increase in cultivated land. Intensification of agricultural land use was more in the villages of the highland zone than in the middleland and lowland zones. Villages of the lowland zone showed a decline of cultivated land area, particularly in the tree crops category, and a constant or declining trend of the natural vegetation coverage – especially grasslands and woodlands.
To reduce unplanned farm expansions into areas of natural vegetation, it is recommended that the Ministry of Agriculture should re-emphasise intercropping practices and provide extension services targeting crops such as potatoes and bananas which are now commercialised. This would be a step towards improving agricultural land productivity and addressing local food security. The ministry of Energy and Minerals could finance the ongoing tree planting efforts by local communities and enhance the use of more efficient charcoal stoves so as not only to protect the remaining forests but also as a way of diversifying the communities’ livelihoods.<br>AFRIKAANSE OPSOMMING: Die Mount Rungwe ekosisteem (MRE) het 'n unieke berggebaseerde hulpbronbasis. Sy biologiese, hidrologiese, ekonomiese en kulturele erfenis bied vele ontwikkelingsgeleenthede vir Tanzanië. Sedert die 1970s het die MRE verandering in grondgebruik ervaar wat implikasies inhou vir bestaanswyses van sy bewoners. Daarom vereis die veranderingsverskynsel wetenskaplike ondersoek na die omvang en aard van grondgebruikveranderinge en die implikasies daarvan vir gemeenskappe se lewensbestaan.
Die doel van die studie was om ondersoek in te stel na die belangrikste veranderinge in grondgebruik en om die drywers verantwoordelik vir hierdie veranderinge te identifiseer en die onderlinge verband tussen die verandering in grondgebruik en gemeenskappe se lewensbestaan te identifiseer. Daaruit word wenslike bestuursopsies duidelik vir die verbetering van landelike bestaansmoontlikhede en die handhawing van ekologiese integriteit van die MRE. 'n Navorsingsontwerp wat beide kwalitatiewe en kwantitatiewe benaderings integreer is gekies. Vir veldwerk is ses dorpe in drie ekologiese sones ondersoek en 384 respondente is ondervra. Inligting oor die grondgebruike, -veranderings, beleide, instellings en prosesse wat die gebied beïnvloed het, is verkry deur middel van vraelyste, onderhoude, veldwaarneming, en dokumentontleding. Satellietbeelde van 1973, 1986, 1991 en 2010 is ontleed vir ruimtelike en temporale patrone van grondgebruik en verandering.
Die bevindinge dui daarop dat die MRE grondgebruik-omskakeling van verskillende kategorieë na ander in veral die hooglandsone ervaar. Regeringsbeleid oor die gebruik en toegang tot natuurlike woude, landbougrond en energiebronne het bygedra tot hierdie grondgebruike en hul veranderinge. Demografiese, kulturele, ekonomiese en omgewingsfaktore, enkel of kumulatief, het ook tot die veranderinge bygedra. Die meeste van die veranderinge in grondgebruik is tussen 1991 en 2010 aangeteken. Op distriksvlak het byvoorbeeld natuurlike plantegroei, veral bosveld en woud, beduidend oor die studietydperk afgeneem, terwyl die bewerkte grondoppervlak sterk toegeneem het. Intensivering van landbougrondgebruik was meer intens in die dorpe van die hooglandsone in vergelyking met die middelland en laer sones. Dorpe van die laer sone het weer 'n afname van bewerkte grond, veral boomagtige gewasse, en 'n konstante of dalende tendens van die natuurlike plantegroei ervaar – veral gras- en bosveld. Om ongewenste plaasuitbreidings na gebiede van natuurlike plantegroei te voorkom, beveel die studie aan dat die landbouministerie weer klem plaas op praktyk vir tussenverbouing van gewasse en voorligtingsdienste voorsien vir die verbouing van gekommersialiseerde gewasse soos aartappels en piesangs. Dit sou die verbetering van die landbou-produktiwiteit en die verhoging van plaaslike voedselsekuriteit in die hand werk. Die energieministerie behoort origens deurlopende boomplant-aksies deur plaaslike gemeenskappe te stimuleer deur verskaffing van finansies en moet die gebruik van meer doeltreffende houtskool stowe aanmoedig. Dit sal die oorblywende woude help beskerm en is ook 'n manier om die gemeenskappe se lewensonderhoudstelsels te diversifiseer en te verbeter.
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Delalande, Manuëlla. "HYDROLOGIE ET GEOCHIMIE ISOTOPIQUE DU LAC MASOKO ET DE LACS VOLCANIQUES DE LA PROVINCE ACTIVE DU RUNGWE (SUD-OUEST TANZANIE)." Phd thesis, Université Paris Sud - Paris XI, 2008. http://tel.archives-ouvertes.fr/tel-00403009.
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Les lacs sont des réservoirs naturels potentiels d'eau douce. Réceptacles d'eaux météoriques ils ne sont plus systématiquement considérés aujourd'hui comme de simple pluviomètre. Véritables lieux de régulation et d'échanges, ils peuvent former des lieux de concentration, accumulateur et véhiculeur de pollutions ou à l'opposé, des milieux de décantation et de dilution favorables à la préservation de la ressource en eau. Cette thèse se focalise sur les aspects quantitatifs et qualitatifs de la réserve en eau douce potentielle du lac Masoko et d'autres lacs volcaniques du Sud Ouest tanzanien pour la plupart peu ou jamais étudiés. Ces travaux ont mis en évidence que, les niveaux et bilans de ces systèmes fermés, sont notamment régis par des échanges avec l'atmosphère positifs dont résultent d'importants flux souterrains et que ces lacs endoréiques, constituent des lieux de dilution. Ces hydro-systèmes présentent également divers degrés et types de minéralisation qui semblent en premier lieu, contrôlés par la contribution d'apports hydrothermaux aux lacs et secondairement par les temps de résidence des eaux lacustres. L'étude des fonctionnements hydrologique et géochimique des lacs du Sud-Ouest tanzanien, sous les conditions hydroclimatiques régionales actuelles (P-E >0), a permis de montrer que le degré de minéralisation des systèmes présentés pourrait s'accroître sous l'influence d'une augmentation de la pluviométrie. Des augmentations de la minéralisation lacustre seraient dans cette région, reliées à des conditions climatiques humides au YD et au LGM, alors qu'elles donnent préférentiellement lieu à des interprétations contraires.
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Delalande, Manuëlla. "Hydrologie et géochimie isotopique du lac Masoko et de lacs volcaniques de la province active du Rungwe (Sud-Ouest Tanzanie)." Paris 11, 2008. https://tel.archives-ouvertes.fr/tel-00403009.
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Les lacs sont des réservoirs naturels potentiels d'eau douce. Réceptacles d'eaux météoriques ils ne sont plus systématiquement considérés aujourd'hui comme de simple pluviomètre. Véritables lieux de régulation et d'échanges, ils peuvent former des lieux de concentration, accumulateur et véhiculeur de pollutions ou à l'opposé, des milieux de décantation et de dilution favorables à la préservation de la ressource en eau. Cette thèse se focalise sur les aspects quantitatifs et qualitatifs de la réserve en eau douce potentielle du lac Masoko et d'autres lacs volcaniques du Sud Ouest tanzanien pour la plupart peu ou jamais étudiés. Ces travaux ont mis en évidence que, les niveaux et bilans de ces systèmes fermés, sont notamment régis par des échanges avec l'atmosphère positifs dont résultent d'importants flux souterrains et que ces lacs endoréiques, constituent des lieux de dilution. Ces hydro-systèmes présentent également divers degrés et types de minéralisation qui semblent en premier lieu, contrôlés par la contribution d'apports hydrothermaux aux lacs et secondairement par les temps de résidence des eaux lacustres. L'étude des fonctionnements hydrologique et géochimique des lacs du Sud-Ouest tanzanien, sous les conditions hydroclimatiques régionales actuelles (P-E >0), a permis de montrer que le degré de minéralisation des systèmes présentés pourrait s'accroître sous l'influence d'une augmentation de la pluviométrie. Des augmentations de la minéralisation lacustre seraient dans cette région, reliées à des conditions climatiques humides au YD et au LGM, alors qu'elles donnent préférentiellement lieu à des interprétations contraires<br>Lakes constitute potential and natural freshwater reservoir which are today not systematically considered anymore as simple pluviometer. Exchange and regulation places, lakes can be places of concentration where polluants accumulate or opposite places of dilution, which are favourable to the preservation of water ressources. This thesis focus on quantitative and qualitative aspects of the potential freswater reserve of Lake Masoko and others volcanic lakes of South West tanzanian few or never studied. This work gives evidence that the lake-levels and the balances of these systems are controlled by positive exchanges with atmosphere from which, result important groundwater fluxes. It was also shown that these mostly closed lakes constitute dilution places. These hydro-systems show also mineralisation degree and type, which appear control by first, the contribution of hydrothermal inflows to the lakes and secondly, by the lake water residence times. This hydrological and geochemical study of South West tanzanian lakes, under actual regional hydroclimatic conditions, allows to show that the mineralization degree of studied systems could rise under increase of precipitation rates or, decrease of evaporation rates; both in favour of the contribution of inflows to the lakes. Lake mineralization increases would be, in this region, linked to wet climatic conditions at YD and LGM whereas opposite interpretations are usually considered
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Njinju, Emmanuel A. "A Geodynamic Investigation of Magma-Poor Rifting Processes and Melt Generation: A Case Study of the Malawi Rift and Rungwe Volcanic Province, East Africa." Diss., Virginia Tech, 2021. http://hdl.handle.net/10919/101867.
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Our understanding of how magma-poor rifts accommodate strain remains limited largely due to sparse geophysical observations from these rift systems. To better understand magma-poor rifting processes, chapter 1 of this dissertation is focused on investigating the lithosphere-asthenosphere interactions beneath the Malawi Rift, a segment of the magma-poor Western Branch of the East African Rift (EAR). Chapter 2 and 3 are focused on investigating the sources of melt beneath the Rungwe Volcanic Province (RVP), an anomalous volcanic center located at the northern tip of the Malawi Rift. In chapter 1, we use the lithospheric structure of the Malawi Rift derived from the World Gravity Model 2012 to constrain three-dimensional (3D) numerical models of lithosphere-asthenosphere interactions, which indicate ~3 cm/yr asthenospheric upwelling beneath the thin lithosphere (115-125 km) of the northern Malawi Rift and the RVP from lithospheric modulated convection (LMC) that is decoupling from surface motions. We suggest that the asthenospheric upwelling may generate decompression melts which weakens the lithosphere thereby enabling extension.
The source of asthenospheric melt for the RVP is still contentious. Some studies suggest the asthenospheric melt beneath the RVP arises from thermal perturbations in the upper mantle associated with plume head materials, while others propose decompression melting from upwelling asthenosphere due to LMC where the lithosphere is thin. Chapter 2 of this dissertation is focused on testing the hypothesis that asthenospheric melt feeding the RVP can be generated from LMC using realistic constraints on the mantle potential temperature (Tp). We develop a 3D thermomechanical model of LMC beneath the RVP and the entire Malawi Rift that incorporates melt generation. We find decompression melt associated with LMC upwelling (~3 cm/yr) occurs at a maximum depth of ~150 km localized beneath the RVP.
Studies of volcanic rock samples from the RVP indicate plume signatures which are enigmatic since the RVP is highly localized, unlike the large igneous provinces in the Eastern Branch of the EAR. In chapter 3, we test the hypothesis that the melt beneath the RVP is generated from plume materials. We investigate melt generation from plume-lithosphere interactions (PLI) beneath the RVP by developing a 3D seismic tomography-based convection (TBC) model beneath the RVP. The seismic constraints indicate excess temperatures of ~250 K in the sublithospheric mantle beneath the RVP suggesting the presence of a plume. We find a relatively fast upwelling (~10 cm/yr) beneath the RVP which we interpret as a rising plume. The TBC upwelling generates decompression melt (~0.25 %) at a maximum depth of ~200 km beneath the RVP where the lithosphere is thinnest (~100 km). Our results demonstrate that an excess heat source from may be plume materials is necessary for melt generation in the sublithospheric mantle beneath the RVP because passive asthenospheric upwelling of ambient mantle will require a higher than normal Tp to generate melt.
Studies of volcanic rock samples from the RVP indicate plume signatures which are enigmatic
since the RVP is highly localized, unlike the large igneous provinces in the Eastern Branch
of the EAR. In chapter 3, we test the hypothesis that the melt beneath the RVP is generated
from plume materials. We investigate melt generation from plume-lithosphere interactions
(PLI) beneath the RVP by developing a 3D seismic tomography-based convection (TBC)
model beneath the RVP. The seismic constraints indicate excess temperatures of ≈ 250K in
the sublithospheric mantle beneath the RVP suggesting the presence of a plume. We find a
relatively fast upwelling (≈10 cm/yr) beneath the RVP which we interpret as a rising plume.
The TBC upwelling generates decompression melt (≈0.25 %) at a maximum depth of ≈200
km beneath the RVP where the lithosphere is thinnest (≈100 km). Our results demonstrate
that an excess heat source from may be plume materials is necessary for melt generation
in the sublithospheric mantle beneath the RVP because passive asthenospheric upwelling of
ambient mantle will require a higher than normal Tp to generate melt.<br>Doctor of Philosophy<br>Studies suggest the presence of hot, melted rock deep in the continents makes them weaker and easier to break apart, however, our understanding of how continents with less melted rock break apart remains limited largely due to sparse geophysical observations from these dry areas. To better understand how continents with less melted rock break apart, chapter 1 of this dissertation is focused on investigating the interactions between the rigid part of the Earth, called lithosphere, and the underlying lower viscosity rock layer called asthenosphere beneath the Malawi Rift, a segment of the magma-poor Western Branch of the East African Rift (EAR). Chapter 2 and 3 are focused on investigating the sources of melt beneath the Rungwe Volcanic Province (RVP), an anomalous volcanic center located at the northern tip of the Malawi Rift. In chapter 1, we use the lithospheric structure of the Malawi Rift derived from gravity data to constrain three-dimensional (3-D) numerical models of lithosphere-asthenosphere interactions, which indicate ~3 cm/yr asthenospheric upwelling beneath the thin lithosphere (115-125 km) of the northern Malawi Rift and the RVP that does not seem to drive movements at the surface. We suggest that the asthenospheric upwelling may generate melted rock which weakens the lithosphere thereby enabling extension.
However, the source of asthenospheric melt for the RVP is still contentious. Some studies suggest the asthenospheric melt beneath the RVP arises from thermal perturbations in the upper mantle associated with rising mantle rocks or plume head materials, while others propose melting occurs from upwelling asthenosphere due to lithospheric modulated convection (LMC) where the lithosphere is thin. Chapter 2 of this dissertation is focused on testing the hypothesis that asthenospheric melt feeding the RVP can be generated from LMC. We develop a 3D thermomechanical model of LMC beneath the RVP and the entire Malawi Rift that incorporates melt generation. We find decompression melt associated with LMC upwelling (~3 cm/yr) occurs at a maximum depth of ~150 km localized beneath the RVP.
Studies of volcanic rock samples from the RVP indicate plume signatures which are enigmatic since the RVP is highly localized, unlike the large igneous provinces in the Eastern Branch of the EAR. In chapter 3, we investigate melt generation from plume-lithosphere interactions (PLI) beneath the RVP. We develop a 3D model of convection using information from seismology we call tomography-based convection (TBC) beneath the RVP. The seismic data indicate excess temperatures of ~250 K beneath the RVP suggesting the presence of a plume. We find a relatively fast upwelling (~10 cm/yr) beneath the RVP which we interpret as a rising plume. The TBC upwelling generates decompression melt at a maximum depth of ~200 km beneath the RVP. Our results demonstrate that an excess heat source from may be plume materials is necessary for melt generation in the sublithospheric mantle beneath the RVP because passive asthenospheric upwelling of ambient mantle will require a higher than normal mantle potential temperatures to generate melt.
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Kroulíková, Tereza. "Runge-Kuttovy metody." Master's thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2018. http://www.nusl.cz/ntk/nusl-392847.
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Tato práce se zabývá Runge--Kuttovými metodami pro počáteční problém. Práce začíná analýzou Eulerovy metody a odvozením podmínek řádu. Jsou představeny modifikované metody. Pro dvě z nich je určen jejich řád teoreticky a pro všechny je provedeno numerické testování řádu. Jsou představeny a numericky testovány dva typy metod s odhadem chyby, "embedded" metody a metody založené na modifikovaných metodách. V druhé části jsou odvozeny implicitní metody. Jsou představeny dva způsoby konstrukce implicitních "embedded" metod. Jsou zmíněny také diagonální implicitní metody. Na závěr jsou probrány dva druhy stability u metod prezentovaných v práci.
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Elmikkawy, M. E. A. "Embedded Runge-Kutta-Nystrom methods." Thesis, Teesside University, 1986. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.371400.
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Warzynski, Andrzej. "Runge-Kutta residual distribution schemes." Thesis, University of Leeds, 2013. http://etheses.whiterose.ac.uk/5271/.
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The residual distribution framework and its ability to carry out genuinely multidimensional upwinding has attracted a lot of research interest in the past three decades. Although not as robust as other widely used approximate methods for solving hyperbolic partial differential equations, when residual distribution schemes do provide a plausible solution it is usually more accurate than in the case of other approaches. Extending these methods to time-dependent problems remains one of the main challenges in the field. In particular, constructing such a solution so that the resulting discretisation exhibits all the desired properties available in the steady state setting. It is generally agreed that there is not yet an ideal generalisation of second order accurate and positive compact residual distribution schemes designed within the steady residual distribution framework to time-dependent problems. Various approaches exist, none of which is considered optimal nor completely satisfactory. In this thesis two possible extensions are constructed, analysed and verified numerically: continuous-in-space and discontinuous-in-space Runge-Kutta Residual Distribution methods. In both cases a Runge-Kutta-type time-stepping method is used to integrate the underlying PDEs in time. These are then combined with, respectively, a continuous- and discontinuous-in-space residual distribution type spatial approximation. In this work a number of second order accurate linear continuous-in-space Runge- Kutta residual distribution methods are constructed, tested experimentally and compared with existing approaches. Additionally, one non-linear second order accurate scheme is presented and verified. This scheme is shown to perform better in the close vicinity of discontinuities (in terms of producing spurious oscillations) when compared to linear second order schemes. The experiments are carried out on a set of structured and unstructured triangular meshes for both scalar linear and nonlinear equations, and for the Euler equations of fluid dynamics as an example of systems of non-linear equations. In the case of the discontinuous-in-space Runge-Kutta residual distribution framework, the thorough analysis presented here highlights a number of shortcomings of this approach and shows that it is not as attractive as initially anticipated. Nevertheless, a rigorous overview of this approach is given. Extensive numerical results on both structured and unstructured triangular meshes confirm the analytical results. Only results for scalar (both linear and non-linear) equations are presented.
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Strasser-Klotz, Susanne. "Runge und Ossian Kunst, Literatur, Farbenlehre /." [S.l. : s.n.], 2005. http://deposit.ddb.de/cgi-bin/dokserv?idn=975068997.
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Gilmore, John Patrick. "Explicit Runge-Kutta global error estimators." Thesis, Teesside University, 1996. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.410876.
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Almeida, Cesar Guilherme de. "SOBRE MÉTODOS DE RUNGE-KUTTA PARALELOS." Universidade de São Paulo, 1993. http://www.teses.usp.br/teses/disponiveis/55/55134/tde-17082018-101023/.
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Esta dissertação de mestrado apresenta um estudo referente a métodos de Runge-Kutta Paralelos. Baseado em alguns artigos sobre o assunto, este trabalho, contém duas técnicas de construção de métodos Paralelos. Uma técnica é utilizar a Teoria das Diferenças Elementares, a outra é recorrer ao processo iterativo diagonal para resolvermos as equações implícitas do método de Runge-Kutta. Também apresentamos resultados numéricos, ou seja, implementamos os métodos construídos a partir de cada uma das técnicas. A linguagem utilizada foi a OCCAM, adequada para programação concorrente. Uma referência é o livro [Poutain, May, 87].<br>This MSc dissertation presents a study on Paralel Runge-Kutta methods. It is based on some papers about the subject and contains two techniques for construction of Paralel methods. The first one uses the Elementary Differential Theory, while the second appeals to a Diagonal Iterated method for solving the implicit equations of the RK method. Numerical results corresponding to both techniques are included. The computer language used was OCCAM, which is adequated to concurrent programming,
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Malek, Fadi. "Formules de type Runge-Kutta-Nystrom." Thesis, University of Ottawa (Canada), 1992. http://hdl.handle.net/10393/7564.
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Explicit Runge-Kutta-Nystrom pairs, which solve directly second order initial value problems of the form $y\sp{\prime\prime}$ = $f(x,y)$ with the first derivative $y\sp\prime$ absent, are considered. Pairs consisting of formulae of order $p-1$ and p, respectively, can be designed to control the local error in y, in $y\sp\prime$ or in y and $y\sp\prime$. They may also advance the numerical approximations using the lower order formulae or the higher order formulae. These two sets of choices lead to five types of pairs. We establish the minimum number of stages required to form the five types of pairs for p = 2, ...,6, by producing an existing pair and disproving the existence of a similar pair with fewer stages. Notions of Nystrom methods and Nystrom trees are recalled along with the order conditions for these methods.
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Runge, Wolfgang [Verfasser]. "Werkzeug Objekt : Kybernetik und Objektorientierung / Wolfgang Runge." Flensburg : Zentrale Hochschulbibliothek Flensburg, 2001. http://d-nb.info/1019138211/34.
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Runge, Tobias [Verfasser]. "Plasmaeigenschaften in Funkenstrecken unter Stoßstrombelastung / Tobias Runge." München : Verlag Dr. Hut, 2018. http://d-nb.info/1166482596/34.
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Wade, Kevin Christopher. "SARK : a type-insensitive Runge-Kutta code." Thesis, University of Greenwich, 1987. http://gala.gre.ac.uk/8709/.
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A novel solution method based on Mono-implicit Runge-Kutta methods has been fully developed and analysed for the numerical solution of stiff systems of ordinary differential equations (ODE). These Backward Runge-Kutta (BRK) methods have very desirable stability properties which make them efficient for solving a certain class of ODE which are not solved adequately by current methods. These stability properties arise from applying a numerical method to the standard test problem and analysing the resulting stability function. This technique, however, fails to show the full potential of a method. With this in mind a new graphical technique has been derived that examines the methods performance on the standard test case in much greater detail. This technique allows a detailed investigation of the characteristics required for a numerical integration of highly oscillatory problems. Numerical ODE solvers are used extensively in engineering applications, where both stiff and non-stiff systems are encountered, hence a single code capable of integrating the two categories, undetected by the user, would be invaluable. The BRK methods, combined with explicit Runge-Kutta (ERK) methods, are incorporated into such a code. The code automatically determines which integrator can currently solve the problem most efficiently. A switch to the most efficient method is then made. Both methods are closely linked to ensure that overheads expended in the switching are minimal. Switching from ERK to BRK is performed by an existing stiffness detection scheme whereas switching from BRK to ERK requires a new numerical method to be devised. The new methods, called extended BRK (EBRK) methods, are based on the BRK methods but are chosen so as to possess stability properties akin to the ERK methods. To make the code more flexible the switching of order is also incorporated. Numerical results from the type-insensitive code, SARK, indicate that it performs better than the most widely used non-stiff solver and is often more efficient than a specialized stiff solver.
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Cereceda, Puyol María Fernanda. "Hidrogeología subterránea de la subcuenca de Rungue, Región Metropolitana." Tesis, Universidad de Chile, 2013. http://www.repositorio.uchile.cl/handle/2250/115251.
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Geóloga<br>El presente documento corresponde a la caracterización hidrogeológica ejecutada en la subcuenca de Rungue emplazada en la hoya del estero Tiltil. Dicho estudio forma parte de la línea base constitutiva de la Evaluación de Impacto Ambiental asociado a un proyecto de disposición de residuos tóxicos y peligrosos, que monitorea la empresa Ciclo S.A.
La subcuenca de Rungue se ubica a 51 km al norte de la ciudad de Santiago y cubre un área de 37,9 km2.Presenta un clima semi-árido, con un promedio de precipitación anual de 371,2 mm y una recarga del acuífero que fluctúa entre los10 y los17 l/s.
En la zona, se reconocieron 3 unidades hidrogeológicas. La primera de ellas está compuesta de rocas volcánicas y sedimentarias de la Formación Las Chilcas, que se encuentran fracturadas en sus 20 m superiores. Esta unidad corresponde al único acuífero del área y, de acuerdo a los antecedentes de 3 ensayos de bombeo realizados, tiene una permeabilidad muy baja. Las unidades hidrogeológicas 2 y 3 corresponden a depósitos coluviales y aluviales, respectivamente. Éstos son de poco espesor, modesta expresión areal y no se presentan saturados.
En las captaciones presentes en la subcuenca, se realizaron mediciones periódicas de niveles freáticos con lo cual se pudo estructurar un mapa de la superficie equipotencial. Según éste, la dirección de escurrimiento del flujo subterráneo, en la zona del predio, es nor-noreste. Luego, hacia aguas abajo, adopta un sentido nor-noroeste en la zona cercana al embalse Rungue.
Con los gradientes hidráulicos definidos y la transmisividad determinada se calculó una velocidad de escurrimiento de 13,46 m/año. Asumiendo dicha velocidad media, el tiempo requerido para que el agua subterránea se desplace desde el predio hasta el área del tranque Rungue sería de unos 300 años aproximadamente.
Considerando que el coeficiente de almacenamiento se ubica en un rango entre 1 y 3% se obtienen valores para el volumen de agua subterránea embalsada entre 3.300.000 y 9.900.000 m3. Éstas, expresadas como caudal continuo para 50 años, corresponden a 2 y 6 l/s, respectivamente.
Por último, se realizaron 4 campañas de muestreo químico con los cuales se concluye que las aguas subterráneas son de tipo cálcicas bicarbonatadas con leve incremento del anión sulfato en sectores que presentan cierto grado de alteración. Si los resultados se comparan con las normas chilenas de Riego y de Agua Potable, se puede asegurar que éstas no cumplen con dichas normativas.
Conforme a lo señalado, se puede aseverar que, desde la perspectiva hidrogeológica, el área es apropiada para construir un vertedero de residuos tóxicos y peligrosos.
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Macdougall, Thomas Anthony. "Global error estimators for explicit Runge-Kutta methods." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1998. http://www.collectionscanada.ca/obj/s4/f2/dsk2/tape15/PQDD_0001/MQ28227.pdf.
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Runge, Jörn [Verfasser]. "Modellierung von Windenergieanlagen für die Netzberechnung / Jörn Runge." Aachen : Shaker, 2008. http://d-nb.info/1162792760/34.
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Storer, Geoffrey. "Global error estimation for Runge-Kutta-Nystrom processes." Thesis, Teesside University, 1990. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.258774.
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Tanner, Gregory Mark. "Generalized additive Runge-Kutta methods for stiff odes." Diss., University of Iowa, 2018. https://ir.uiowa.edu/etd/6507.
Full textAbstract:
In many applications, ordinary differential equations can be additively partitioned
\[y'=f(y)=\sum_{m=1}^{N}\f{}{m}(y).]
It can be advantageous to discriminate between the different parts of the right-hand side according to stiffness, nonlinearity, evaluation cost, etc. In 2015, Sandu and G\"{u}nther \cite{sandu2015gark} introduced Generalized Additive Runge-Kutta (GARK) methods which are given by
\begin{eqnarray*}
Y_{i}^{\{q\}} & = & y_{n}+h\sum_{m=1}^{N}\sum_{j=1}^{s^{\{m\}}}a_{i,j}^{\{q,m\}}f^{\{m\}}\left(Y_{j}^{\{m\}}\right)\\
& & \text{for } i=1,\dots,s^{\{q\}},\,q=1,\dots,N\\
y_{n+1} & = & y_{n}+h\sum_{m=1}^{N}\sum_{j=1}^{s^{\{m\}}}b_{j}^{\{m\}}f^{\{m\}}\left(Y_{j}^{\{m\}}\right)\end{eqnarray*}
with the corresponding generalized Butcher tableau
\[\begin{array}{c|ccc} \c{}{1} & \A{1,1} & \cdots & \A{1,N}\\\vdots & \vdots & \ddots & \vdots\\
\c{}{N} & \A{N,1} & \cdots & \A{N,N}\\\hline & \b{}{1} & \cdots & \b{}{N}\end{array}\]
The diagonal blocks $\left(\A{q,q},\b{}{q},\c{}{q}\right)$ can be chosen for example from standard Runge-Kutta methods, and the off-diagonal blocks $\A{q,m},\:q\neq m,$ act as coupling coefficients between the underlying methods. The case when $N=2$ and both diagonal blocks are implicit methods (IMIM) is examined.
This thesis presents order conditions and simplifying assumptions that can be used to choose the off-diagonal coupling blocks for IMIM methods. Error analysis is performed for stiff problems of the form
\begin{eqnarray*}\dot{y} & = & f(y,z)\\
\epsilon\dot{z} & = & g(y,z)\end{eqnarray*}
with small stiffness parameter $\epsilon.$ As $\epsilon\to 0,$ the problem reduces to an index 1 differential algebraic equation provided
$g_{z}(y,z)$ is invertible in a neighborhood of the solution. A tree theory is developed for IMIM methods applied to the reduced problem. Numerical results will be presented for several IMIM methods applied to the Van der Pol equation.
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Ijaz, Muhammad. "Implicit runge-kutta methods to simulate unsteady incompressible flows." Texas A&M University, 2007. http://hdl.handle.net/1969.1/85850.
Full textAbstract:
A numerical method (SIMPLE DIRK Method) for unsteady incompressible
viscous flow simulation is presented. The proposed method can be used to achieve
arbitrarily high order of accuracy in time-discretization which is otherwise limited to
second order in majority of the currently used simulation techniques. A special class of
implicit Runge-Kutta methods is used for time discretization in conjunction with finite
volume based SIMPLE algorithm. The algorithm was tested by solving for velocity field
in a lid-driven square cavity. In the test case calculations, power law scheme was used in
spatial discretization and time discretization was performed using a second-order implicit
Runge-Kutta method. Time evolution of velocity profile along the cavity centerline was
obtained from the proposed method and compared with that obtained from a commercial
computational fluid dynamics software program, FLUENT 6.2.16. Also, steady state
solution from the present method was compared with the numerical solution of Ghia, Ghia,
and Shin and that of Erturk, Corke, and Goökçöl. Good agreement of the solution of the
proposed method with the solutions of FLUENT; Ghia, Ghia, and Shin; and Erturk, Corke,
and Goökçöl establishes the feasibility of the proposed method.
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Stumpp, Thomas. "Integration stark gedämpfter mechanischer Systeme mit Runge-Kutta-Verfahren." [S.l. : s.n.], 2004. http://deposit.ddb.de/cgi-bin/dokserv?idn=971542597.
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Fletcher, Matthew T. "Discovery and optimization of low-storage Runge-Kutta methods." Thesis, Monterey, California: Naval Postgraduate School, 2015. http://hdl.handle.net/10945/45852.
Full textAbstract:
Approved for public release; distribution is unlimited<br>Runge-Kutta (RK) methods are an important family of iterative methods for approximating the solutions of ordinary differential equations (ODEs) and differential algebraic equations (DAEs). It is common to use an RK method to discretize in time when solving time dependent partial differential equations (PDEs) with a method-of-lines approach as in Maxwell’s Equations. Different types of PDEs are discretized in such a way that could result in a high dimensional ODE or DAE.We use a low-storage RK (LSRK) method that stores two registers per ODE dimension, which limits the impact of increased storage requirements. Classical RK methods, however, have one storage variable per stage. In this thesis we compare the efficiency and accuracy of LSRK methods to RK methods. We then focus on optimizing the truncation error coefficients for LSRK to discover new methods. Reusing the tools from the optimization method, we discover new methods for low-storage half-explicit RK (LSHERK) methods for solving DAEs.
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Runge, Charlotte [Verfasser]. "Molekulargenetische Ursachen von mentaler Retardierung mit Epilepsie / Charlotte Runge." Lübeck : Zentrale Hochschulbibliothek Lübeck, 2014. http://d-nb.info/1047115670/34.
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Lui, Ho Man. "Runge-Kutta Discontinuous Galerkin method for the Boltzmann equation." Thesis, Massachusetts Institute of Technology, 2006. http://hdl.handle.net/1721.1/39215.
Full textAbstract:
Thesis (S.M.)--Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2006.<br>Includes bibliographical references (p. 85-87).<br>In this thesis we investigate the ability of the Runge-Kutta Discontinuous Galerkin (RKDG) method to provide accurate and efficient solutions of the Boltzmann equation. Solutions of the Boltzmann equation are desirable in connection to small scale science and technology because when characteristic flow length scales become of the order of, or smaller than, the molecular mean free path, the Navier-Stokes description fails. The prevalent Boltzmann solution method is a stochastic particle simulation scheme known as Direct Simulation Monte Carlo (DSMC). Unfortunately, DSMC is not very effective in low speed flows (typical of small scale devices of interest) because of the high statistical uncertainty associated with the statistical sampling of macroscopic quantities employed by this method. This work complements the recent development of an efficient low noise method for calculating the collision integral of the Boltzmann equation, by providing a high-order discretization method for the advection operator balancing the collision integral in the Boltzmann equation. One of the most attractive features of the RKDG method is its ability to combine high-order accuracy, both in physical space and time, with the ability to capture discontinuous solutions.<br>(cont.) The validity of this claim is thoroughly investigated in this thesis. It is shown that, for a model collisionless Boltzmann equation, high-order accuracy can be achieved for continuous solutions; whereas for discontinuous solutions, the RKDG method, with or without the application of a slope limiter such as a viscosity limiter, displays high-order accuracy away from the vicinity of the discontinuity. Given these results, we developed a RKDG solution method for the Boltzmann equation by formulating the collision integral as a source term in the advection equation. Solutions of the Boltzmann equation, in the form of mean velocity and shear stress, are obtained for a number of characteristic flow length scales and compared to DSMC solutions. With a small number of elements and a low order of approximation in physical space, the RKDG method achieves similar results to the DSMC method. When the characteristic flow length scale is small compared to the mean free path (i.e. when the effect of collisions is small), oscillations are present in the mean velocity and shear stress profiles when a coarse velocity space discretization is used. With a finer velocity space discretization, the oscillations are reduced, but the method becomes approximately five times more computationally expensive.<br>(cont.) We show that these oscillations (due to the presence of propagating discontinuities in the distribution function) can be removed using a viscosity limiter at significantly smaller computational cost.<br>by Ho Man Lui.<br>S.M.
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Fenton, P. "The dynamics of variable time-stepping Runge-Kutta methods." Thesis, University of Sussex, 2002. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.394994.
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Runge, Pia [Verfasser]. "Altersabhängige Aktivierungsmuster in der funktionellen Kernspintomographie nach Sacculusstimulation / Pia Runge." Mainz : Universitätsbibliothek Mainz, 2017. http://d-nb.info/1124105530/34.
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Schaub, Meike. "Numerische Integration steifer mechanischer Systeme mit impliziten Runge-Kutta-Verfahren." [S.l. : s.n.], 2004. http://deposit.ddb.de/cgi-bin/dokserv?idn=970967322.
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Runge, Franziska [Verfasser]. "Einfluss der NOD1-Aktivierung auf die allergeninduzierte Atemwegsinflammation / Franziska Runge." Berlin : Medizinische Fakultät Charité - Universitätsmedizin Berlin, 2010. http://d-nb.info/1024364895/34.
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Gerlach-Runge, Undine Ariane [Verfasser]. "Managing immunological challenges in intestinal transplantation / Undine Ariane Gerlach-Runge." Berlin : Medizinische Fakultät Charité - Universitätsmedizin Berlin, 2017. http://d-nb.info/1124465308/34.
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Runge, Kristin [Verfasser]. "Die Entwicklung der chirurgischen Behandlung bei rhegmatogener Netzhautablösung / Kristin Runge." Greifswald : Universitätsbibliothek Greifswald, 2014. http://d-nb.info/1047569213/34.
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Mugg, Patrick R. "Construction and Analysis of Multi-Rate Partitioned Runge-Kutta Methods." Thesis, Monterey, California. Naval Postgraduate School, 2012. http://hdl.handle.net/10945/7390.
Full textAbstract:
Adaptive mesh refinement (AMR) of hyperbolic systems allows us to refine the spatial grid of an initial value problem (IVP), in order to obtain better accuracy and improved efficiency of the numerical method being used. However, the solutions obtained are still limited to the local Courant-Friedrichs-Lewy (CFL) time-step restrictions of the smallest element within the spatial domain. Therefore, we look to construct a multi-rate time-integration scheme capable of solving an IVP within each spatial sub-domain that is congruent with that sub-domains respective time-step size. The primary objective for this research is to construct a multi-rate method for use with AMR. In this thesis we will focus on constructing a 2nd order, multi-rate partitioned Runge-Kutta (MPRK2) scheme, such that the non-uniform mesh is constructed with the coarse and fine elements at a two-to-one ratio. We will use general 2nd and 4th order finite differences (FD) methods for non-uniform grids to discretize the spatial derivative, and then use this model to compare the MPRK2 time-integrator against three explicit, 2nd order, single-rate time-integrators Adams-Bashforth 2 (AB2), Backward Differentiation Formula 2 (BDF2), and Runge-Kutta 2 (RK2).
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Runge, Jörg [Verfasser]. "Netzwerkmodell zur Planung von Anlagen mit Fahrerlosen Flurförderzeugen / Jörg Runge." Aachen : Shaker, 2006. http://d-nb.info/116651384X/34.
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Rokhzadi, Arman. "IMEX and Semi-Implicit Runge-Kutta Schemes for CFD Simulations." Thesis, Université d'Ottawa / University of Ottawa, 2018. http://hdl.handle.net/10393/37957.
Full textAbstract:
Numerical Weather Prediction (NWP) and climate models parametrize the effects of boundary-layer turbulence as a diffusive process, dependent on a diffusion coefficient, which appears as nonlinear terms in the governing equations. In the advection dominated zone of the boundary layer and in the free atmosphere, the air flow supports different wave motions, with the fastest being the sound waves. Time integrations of these terms, in both zones, need to be implicit otherwise they impractically restrict the stable time step sizes. At the same time, implicit schemes may lose accuracy compared to explicit schemes in the same level, which is due to dispersion error associated with these schemes. Furthermore, the implicit schemes need iterative approaches like the Newton-Raphson method. Therefore, the combination of implicit and explicit methods, called IMEX or semi-implicit, has extensively attracted attention. In the combined method, the linear part of the equation as well as the fast wave terms are treated by the implicit part and the rest is calculated by the explicit scheme. Meanwhile, minimizing the dissipation and dispersion errors can enhance the performance of time integration schemes, since the stability and accuracy will be restricted by these inevitable errors.
Hence, the target of this thesis is to increase the stability range, while obtaining accurate solutions by using IMEX and semi-implicit time integration methods. Therefore, a comprehensive effort has been made toward minimizing the numerical errors to develop new Runge-Kutta schemes, in IMEX and semi-implicit forms, to temporally integrate the governing equations in the atmospheric field so that the stability is extended and accuracy is improved, compared to the previous schemes.
At the first step, the A-stability and the Strong Stability Preserving (SSP) optimized properties were compared as two essential properties of the time integration schemes. It was shown that both properties attempt to minimize the dissipation and dispersion errors, but in two different aspects. The SSP optimized property focuses on minimizing the errors to increase the accuracy limits, while the A-stability property tries to extend the range of stability. It was shown that the combination of both properties is essential in the field of interest. Moreover, the A-stability property was found as an essential property to accelerate the steady state solutions.
Afterward, the dissipation and dispersion errors, generated by three-stage second order IMEX Runge-Kutta scheme were minimized, while the proposed scheme, so called IMEX-SSP2(2,3,2) enjoys the A-stability and SSP properties. A practical governing equation set in the atmospheric field, so called compressible Boussinesq equations set, was calculated using the new IMEX scheme and the results were compared to one well-known IMEX scheme in the literature, i.e. ARK2(2,3,2), which is an abbreviation of Additive Runge-Kutta. Note that, the ARK2(2,3,2) was compared to various types of IMEX Runge-Kutta schemes and it was found as the more efficient scheme in the atmospheric fields (Weller et al., 2013). It was shown that the IMEX-SSP2(2,3,2) could improve the accuracy and extend the range of stable time step sizes as well. Through the van der Pol test case, it was shown that the ARK2(2,3,2) with L-stability property may decline to the first order in the calculation of stiff limit, while IMEX-SSP2(2,3,2), with A-stability property, is able to retain the assigned second order of accuracy. Therefore, it was concluded that the L-stability property, due to restrictive conditions associated with, may weaken the time integration’s performance, compared to the A-stability property. The ability of the IMEX-SSP2(2,3,2) was proved in solving different case, which is the inviscid Burger equation in spherical coordinate system by using a realistic initial condition dataset.
In the next step, it was attempted to maximize the non-negativity property associated with the numerical stability function of three-stage third order Diagonally Implicit Runge-Kutta (DIRK) schemes. It was shown that the non-negativity has direct relation with non-oscillatory behaviors. Two new DIRK schemes with A- and L-stability properties, respectively, were developed and compared to the SSP(3,3), which obtains the SSP optimized property in the same class of DIRK schemes. The SSP optimized property was found to be more beneficial for the inviscid (advection dominated) flows, since in the von Neumann stability analysis, the SSP optimized property provides more nonnegative region for the imaginary component of the stability function. However, in most practical cases, i.e. the viscous (advection diffusion) flows, the nonnegative property is needed for both real and imaginary components of the stability function. Therefore, the SSP optimized property, individually, is not helpful, unless mixed with the A-stability property. Meanwhile, the A- and L-stability properties were compared as well. The intention is to find how these properties influence the DIRK schemes’ performances. The A-stability property was found as preserving the SSP property more than the L-stability property. Moreover, the proposed A-stable scheme tolerates larger Courant Friedrichs Lewy (CFL) number, while preserving the accuracy and non-oscillatory computations. This fact was proved in calculating different test cases, including compressible Euler and nonlinear viscous Burger equations.
Finally, the time integration of the boundary layer flows was investigated as well. The nonlinearity associated with the diffusion coefficient makes the implicit scheme impractical, while the explicit scheme inefficiently limits the stable time step sizes. By using the DIRK scheme, a new semi-implicit approach was proposed, in which the diffusion coefficient at each internal stage is calculated by a weight-averaged combination of the solutions at current internal stage and previous time step, in which the time integration can benefit from both explicit and implicit advantages. As shown, the accuracy was improved, which is due to engaging the explicit solutions and the stability was extended due to taking advantages of implicit scheme. It was found that the nominated semi-implicit method results in less dissipation error, more accurate solutions and less CPU time usage, compared to the implicit schemes, and it enjoys larger range of stable time steps than other semi-implicit approaches in the literature.
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Small, Scott Joseph. "Runge-Kutta type methods for differential-algebraic equations in mechanics." Diss., University of Iowa, 2011. https://ir.uiowa.edu/etd/1082.
Full textAbstract:
Differential-algebraic equations (DAEs) consist of mixed systems of ordinary differential equations (ODEs) coupled with linear or nonlinear equations. Such systems may be viewed as ODEs with integral curves lying in a manifold. DAEs appear frequently in applications such as classical mechanics and electrical circuits. This thesis concentrates on systems of index 2, originally index 3, and mixed index 2 and 3.
Fast and efficient numerical solvers for DAEs are highly desirable for finding solutions. We focus primarily on the class of Gauss-Lobatto SPARK methods. However, we also introduce an extension to methods proposed by Murua for solving index 2 systems to systems of mixed index 2 and 3. An analysis of these methods is also presented in this thesis. We examine the existence and uniqueness of the proposed numerical solutions, the influence of perturbations, and the local error and global convergence of the methods.
When applied to index 2 DAEs, SPARK methods are shown to be equivalent to a class of collocation type methods. When applied to originally index 3 and mixed index 2 and 3 DAEs, they are equivalent to a class of discontinuous collocation methods. Using these equivalences, (s,s)--Gauss-Lobatto SPARK methods can be shown to be superconvergent of order 2s.
Symplectic SPARK methods applied to Hamiltonian systems with holonomic constraints preserve well the total energy of the system. This follows from a backward error analysis approach. SPARK methods and our proposed EMPRK methods are shown to be Lagrange-d'Alembert integrators.
This thesis also presents some numerical results for Gauss-Lobatto SPARK and EMPRK methods. A few problems from mechanics are considered.
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Auffredic, Jérémy. "A second order Runge–Kutta method for the Gatheral model." Thesis, Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:mdh:diva-49170.
Full textAbstract:
In this thesis, our research focus on a weak second order stochastic Runge–Kutta method applied to a system of stochastic differential equations known as the Gatheral Model. We approximate numerical solutions to this system and investigate the rate of convergence of our method. Both call and put options are priced using Monte-Carlo simulation to investigate the order of convergence. The numerical results show that our method is consistent with the theoretical order of convergence of the Monte-Carlo simulation. However, in terms of the Runge-Kutta method, we cannot accept the consistency of our method with the theoretical order of convergence without further research.
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Biehn, Neil David. "Implicit Runge-Kutta Methods for Stiff and Constrained Optimal Control Problems." NCSU, 2001. http://www.lib.ncsu.edu/theses/available/etd-20010322-165913.
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<p>The purpose of the research presented in this thesis is to better understand and improve direct transcription methods for stiff and state constrained optimal control problems. When some implicit Runge-Kutta methods are implemented as approximations to the dynamics of an optimal control problem, a loss of accuracy occurs when the dynamics are stiff or constrained. A new grid refinement strategy which exploits the variation of accuracy is discussed. In addition, the use of a residual function in place of classical error estimation techniques is proven to work well for stiff systems. Computational experience reveals the improvement in efficiency and reliability when the new strategies are incorporated as part of a direct transcription algorithm. For index three differential-algebraic equations, the solutions of some implicit Runge-Kutta methods may not converge. However, computational experience reveals apparent convergence for the same methods used when index three state inequality constraints become active. It is shown that the solution chatters along the constraint boundary allowing for better approximations. Moreover, the consistency of the nonlinear programming problem formed by a direct transcription algorithm using an implicit Runge-Kutta approximation is proven for state constraints of arbitrary index.<P>
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Roosen-Runge, Felix Verfasser], and Frank [Akademischer Betreuer] [Schreiber. "Salt Effects in Protein Solutions / Felix Roosen-Runge ; Betreuer: Frank Schreiber." Tübingen : Universitätsbibliothek Tübingen, 2014. http://d-nb.info/1162970111/34.
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Pornsawad, Pornsarp, and Christine Böckmann. "Modified iterative Runge-Kutta-type methods for nonlinear ill-posed problems." Universität Potsdam, 2014. http://opus.kobv.de/ubp/volltexte/2014/7083/.
Full textAbstract:
This work is devoted to the convergence analysis of a modified Runge-Kutta-type
iterative regularization method for solving nonlinear ill-posed problems under a priori and a posteriori stopping rules. The convergence rate results of the proposed method can be obtained under Hölder-type source-wise condition if the Fréchet derivative is properly scaled and locally Lipschitz continuous. Numerical results are achieved by using the Levenberg-Marquardt and Radau methods.
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Fontana, Andrea. "Dimostrazioni classiche dei teoremi di approssimazione di Runge nel piano complesso." Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2010. http://amslaurea.unibo.it/1365/.
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Ramos, Manoel Wallace Alves. "Métodos de Euler e Runge-Kutta: uma análise utilizando o Geogebra." Universidade Federal da Paraíba, 2017. http://tede.biblioteca.ufpb.br:8080/handle/tede/9381.
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Previous issue date: 2017-06-19<br>Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES<br>Is evident the importance of ordinary differential equations in modeling problems
in several areas of science. Coupled with this, is increasing the use of numerical
methods to solve such equations. Computers have become an extremely useful tool
in the study of differential equations, since through them it is possible to execute
algorithms that construct numerical approximations for solutions of these equati-
ons. This work introduces the study of numerical methods for ordinary differential
equations presenting the numerical Eulerºs method, improved Eulerºs method and
the class of Runge-Kuttaºs methods. In addition, in order to collaborate with the
teaching and learning of such methods, we propose and show the construction of
an applet created from the use of Geogebm software tools. The applet provides
approximate numerical solutions to an initial value problem, as well as displays the
graphs of the solutions that are obtained from the numerical Eulerºs method, im-
proved Eulerºs method, and fourth-order Runge-Kuttaºs method.<br>É evidente a importancia das equações diferenciais ordinarias na modelagem de
problemas em diversas áreas da ciência, bem como o uso de métodos numéricos para
resolver tais equações. Os computadores são uma ferramenta extremamente útil no
estudo de equações diferenciais, uma vez que através deles é possível executar algo-
ritmos que constroem aproximações numéricas para soluções destas equações. Este
trabalho é uma introdução ao estudo de métodos numéricos para equações diferen-
ciais ordinarias. Apresentamos os métodos numéricos de Euler, Euler melhorado e a
classe de métodos de Runge-Kutta. Além disso, com o propósito de colaborar com o
ensino e aprendizagem de tais métodos, propomos e mostramos a construção de um
applet criado a partir do uso de ferramentas do software Geogebra. O applet fornece
soluções numéricas aproximadas para um problema de valor inicial, bem como eXibe
os graficos das soluções que são obtidas a partir dos métodos numéricos de Euler,
Euler melhorado e Runge-Kutta de quarta ordem.
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Saleh, Ali, and Ahmad Al-Kadri. "Option pricing under Black-Scholes model using stochastic Runge-Kutta method." Thesis, Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, 2021. http://urn.kb.se/resolve?urn=urn:nbn:se:mdh:diva-53783.
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The purpose of this paper is solving the European option pricing problem under the Black–Scholes model. Our approach is to use the so-called stochastic Runge–Kutta (SRK) numericalscheme to find the corresponding expectation of the functional to the stochastic differentialequation under the Black–Scholes model. Several numerical solutions were made to study howquickly the result converges to the theoretical value. Then, we study the order of convergenceof the SRK method with the help of MATLAB.
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Mohr, Darin Griffin. "Hybrid Runge-Kutta and quasi-Newton methods for unconstrained nonlinear optimization." Diss., University of Iowa, 2011. https://ir.uiowa.edu/etd/1249.
Full textAbstract:
Finding a local minimizer in unconstrained nonlinear optimization and a fixed point of a gradient system of ordinary differential equations (ODEs) are two closely related problems. Quasi-Newton algorithms are widely used in unconstrained nonlinear optimization while Runge-Kutta methods are widely used for the numerical integration of ODEs. In this thesis, hybrid algorithms combining low-order implicit Runge-Kutta methods for gradient systems and quasi-Newton type updates of the Jacobian matrix such as the BFGS update are considered. These hybrid algorithms numerically approximate the gradient flow, but the exact Jacobian matrix is not used to solve the nonlinear system at each step. Instead, a quasi-Newton matrix is used to approximate the Jacobian matrix and matrix-vector multiplications are performed in a limited memory setting to reduce storage, computations, and the need to calculate Jacobian information. For hybrid algorithms based on Runge-Kutta methods of order at least two, a curve search is implemented instead of the standard line search used in quasi-Newton algorithms. Stepsize control techniques are also performed to control the stepsize associated with the underlying Runge-Kutta method. These hybrid algorithms are tested on a variety of test problems and their performance is compared with that of the limited memory BFGS algorithm.
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Booth, Andrew S. "Collocation methods for a class of second order initial value problems with oscillatory solutions." Thesis, Durham University, 1993. http://etheses.dur.ac.uk/5664/.
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We derive and analyse two families of multistep collocation methods for periodic initial-value problems of the form y" = f(x, y); y((^x)o) = yo, y(^1)(xo) = zo involving ordinary differential equations of second order in which the first derivative does not appear explicitly. A survey of recent results and proposed numerical methods is given in chapter 2. Chapter 3 is devoted to the analysis of a family of implicit Chebyshev methods proposed by Panovsky k Richardson. We show that for each non-negative integer r, there are two methods of order 2r from this family which possess non-vanishing intervals of periodicity. The equivalence of these methods with one-step collocation methods is also established, and these methods are shown to be neither P-stable nor symplectic. In chapters 4 and 5, two families of multistep collocation methods are derived, and their order and stability properties are investigated. A detailed analysis of the two-step symmetric methods from each class is also given. The multistep Runge-Kutta-Nystrom methods of chapter 4 are found to be difficult to analyse, and the specific examples considered are found to perform poorly in the areas of both accuracy and stability. By contrast, the two-step symmetric hybrid methods of chapter 5 are shown to have excellent stability properties, in particular we show that all two-step 27V-point methods of this type possess non-vanishing intervals of periodicity, and we give conditions under which these methods are almost P-stable. P-stable and efficient methods from this family are obtained and demonstrated in numerical experiments. A simple, cheap and effective error estimator for these methods is also given.
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Keeping, Benjamin Rolf. "Efficient solution methods for large systems of differential-algebraic equations." Thesis, Imperial College London, 1996. http://hdl.handle.net/10044/1/8851.
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Runge, Julian [Verfasser]. "Applications of Advanced Analytics to the Promotion of Freemium Goods / Julian Runge." Berlin : Humboldt-Universität zu Berlin, 2020. http://d-nb.info/1219507601/34.
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Edgar, Christopher A. "An adaptive Runge-Kutta-Fehlberg method for time-dependent discrete ordinate transport." Diss., Georgia Institute of Technology, 2015. http://hdl.handle.net/1853/53935.
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This dissertation focuses on the development and implementation of a new method to solve the time-dependent form of the linear Boltzmann transport equation for reactor transients. This new method allows for a stable solution to the fully explicit form of the transport equation with delayed neutrons by employing an error-controlled, adaptive Runge-Kutta-Fehlberg (RKF) method to differentiate the time domain. Allowing for the time step size to vary adaptively and as needed to resolve the time-dependent behavior of the angular flux and neutron precursor concentrations. The RKF expansion of the time domain occurs at each point and is coupled with a Source Iteration to resolve the spatial behavior of the angular flux at the specified point in time. The decoupling of the space and time domains requires the application of a quasi-static iteration between solving the time domain using adaptive RKF with error control and resolving the space domain with a Source Iteration sweep. The research culminated with the development of the 1-D Adaptive Runge-Kutta Time-Dependent Transport code (ARKTRAN-TD), which successfully implemented the new method and applied it to a suite of reactor transient benchmarks.
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Anne, Cheikh Amadou Tidiane [Verfasser], Jürgen [Akademischer Betreuer] Runge, and Jürgen [Akademischer Betreuer] Wunderlich. "Stratigraphy and properties of soil profiles along transects in Burkina Faso and Benin and their influence on phytodiversity / Cheikh Amadou Tidiane Anne. Gutachter: Jürgen Runge ; Jürgen Wunderlich. Betreuer: Jürgen Runge." Frankfurt am Main : Univ.-Bibliothek Frankfurt am Main, 2013. http://d-nb.info/1045005185/34.
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Higham, D. J. "Error control in nonstiff initial value solvers." Thesis, University of Manchester, 1988. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.234210.
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Keeve, Michael Octavis. "Study and implementation of Gauss Runge-Kutta schemes and application to Riccati equations." Diss., Georgia Institute of Technology, 1997. http://hdl.handle.net/1853/30956.
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Debrabant, Kristian. "Numerische Behandlung linearer und semilinearer partieller differentiell-algebraischer Systeme mit Runge-Kutta-Methoden." [S.l. : s.n.], 2004. http://deposit.ddb.de/cgi-bin/dokserv?idn=97414178X.
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