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Дисертації з теми "Partial Numerical solutions"

Автор: Grafiati

Опубліковано: 4 червня 2021

Оновлено: 24 січня 2023

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1

Bratsos, A. G. "Numerical solutions of nonlinear partial differential equations." Thesis, Brunel University, 1993. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.332806.

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2

Sundqvist, Per. "Numerical Computations with Fundamental Solutions." Doctoral thesis, Uppsala : Acta Universitatis Upsaliensis : Univ.-bibl. [distributör], 2005. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-5757.

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3

Kwok, Ting On. "Adaptive meshless methods for solving partial differential equations." HKBU Institutional Repository, 2009. http://repository.hkbu.edu.hk/etd_ra/1076.

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4

Postell, Floyd Vince. "High order finite difference methods." Diss., Georgia Institute of Technology, 1990. http://hdl.handle.net/1853/28876.

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5

Luo, Wuan Hou Thomas Y. "Wiener chaos expansion and numerical solutions of stochastic partial differential equations /." Diss., Pasadena, Calif. : Caltech, 2006. http://resolver.caltech.edu/CaltechETD:etd-05182006-173710.

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6

Zhang, Jiwei. "Local absorbing boundary conditions for some nonlinear PDEs on unbounded domains." HKBU Institutional Repository, 2009. http://repository.hkbu.edu.hk/etd_ra/1074.

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7

Cheung, Ka Chun. "Meshless algorithm for partial differential equations on open and singular surfaces." HKBU Institutional Repository, 2016. https://repository.hkbu.edu.hk/etd_oa/278.

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Анотація:

Radial Basis function (RBF) method for solving partial differential equation (PDE) has a lot of applications in many areas. One of the advantages of RBF method is meshless. The cost of mesh generation can be reduced by playing with scattered data. It can also allow adaptivity to solve some problems with special feature. In this thesis, RBF method will be considered to solve several problems. Firstly, we solve the PDEs on surface with singularity (folded surface) by a localized method. The localized method is a generalization of finite difference method. A priori error estimate for the discreit

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8

Al-Muslimawi, Alaa Hasan A. "Numerical analysis of partial differential equations for viscoelastic and free surface flows." Thesis, Swansea University, 2013. https://cronfa.swan.ac.uk/Record/cronfa42876.

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9

ROEHL, NITZI MESQUITA. "NUMERICAL SOLUTIONS FOR SHAPE OPTIMIZATION PROBLEMS ASSOCIATED WITH ELLIPTIC PARTIAL DIFFERENTIAL EQUATIONS." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 1991. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=9277@1.

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COORDENAÇÃO DE APERFEIÇOAMENTO DO PESSOAL DE ENSINO SUPERIOR<br>Essa dissertação visa à obtenção de soluções numéricas para problemas de otimização de formas geométricas associados a equações diferenciais parciais elípticas. A principal motivação é um problema termal, onde deseja-se determinar a fronteira ótima, para um volume de material isolante fixo, tal que a perda de calor de um corpo seja minimizada. Realiza-se a análise e implementação numérica de uma abordagem via método das penalidades dos problemas de minimização. O método de elementos finitos é utilizado para discretizar o

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10

Zeng, Suxing. "Numerical solutions of boundary inverse problems for some elliptic partial differential equations." Morgantown, W. Va. : [West Virginia University Libraries], 2009. http://hdl.handle.net/10450/10345.

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Thesis (Ph. D.)--West Virginia University, 2009.<br>Title from document title page. Document formatted into pages; contains v, 58 p. : ill. (some col.). Includes abstract. Includes bibliographical references (p. 56-58).

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11

Murali, Vasanth Kumar. "Code verification using the method of manufactured solutions." Master's thesis, Mississippi State : Mississippi State University, 2002. http://library.msstate.edu/etd/show.asp?etd=etd-11112002-121649.

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12

Bujok, Karolina Edyta. "Numerical solutions to a class of stochastic partial differential equations arising in finance." Thesis, University of Oxford, 2013. http://ora.ox.ac.uk/objects/uuid:d2e76713-607b-4f26-977a-ac4df56d54f2.

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We propose two alternative approaches to evaluate numerically credit basket derivatives in a N-name structural model where the number of entities, N, is large, and where the names are independent and identically distributed random variables conditional on common random factors. In the ﬁrst framework, we treat a N-name model as a set of N Bernoulli random variables indicating a default or a survival. We show that certain expected functionals of the proportion L<sub>N</sub> of variables in a given state converge at rate 1/N as N [right arrow - infinity]. Based on these results, we propose a mult

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13

He, Chuan. "Numerical solutions of differential equations on FPGA-enhanced computers." [College Station, Tex. : Texas A&M University, 2007. http://hdl.handle.net/1969.1/ETD-TAMU-1248.

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14

Yang, Xue-Feng. "Extensions of sturm-liouville theory : nodal sets in both ordinary and partial differential equations." Diss., Georgia Institute of Technology, 1995. http://hdl.handle.net/1853/28021.

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15

Qiao, Zhonghua. "Numerical solution for nonlinear Poisson-Boltzmann equations and numerical simulations for spike dynamics." HKBU Institutional Repository, 2006. http://repository.hkbu.edu.hk/etd_ra/727.

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16

何正華 and Ching-wah Ho. "Iterative methods for the Robbins problem." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2000. http://hub.hku.hk/bib/B31222572.

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17

Li, Siqing. "Kernel-based least-squares approximations: theories and applications." HKBU Institutional Repository, 2018. https://repository.hkbu.edu.hk/etd_oa/539.

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Анотація:

Kernel-based meshless methods for approximating functions and solutions of partial differential equations have many applications in engineering fields. As only scattered data are used, meshless methods using radial basis functions can be extended to complicated geometry and high-dimensional problems. In this thesis, kernel-based least-squares methods will be used to solve several direct and inverse problems. In chapter 2, we consider discrete least-squares methods using radial basis functions. A general l^2-Tikhonov regularization with W_2^m-penalty is considered. We provide error estimates th

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18

Zhou, Jian Ming. "A multi-grid method for computation of film cooling." Thesis, University of British Columbia, 1990. http://hdl.handle.net/2429/29414.

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Анотація:

This thesis presents a multi-grid scheme applied to the solution of transport equations in turbulent flow associated with heat transfer. The multi-grid scheme is then applied to flow which occurs in the film cooling of turbine blades. The governing equations are discretized on a staggered grid with the hybrid differencing scheme. The momentum and continuity equations are solved by a nonlinear full multi-grid scheme with the SIMPLE algorithm as a relaxation smoother. The turbulence k — Є equations and the thermal energy equation are solved on each grid without multi-grid correction. Observatio

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19

Pitts, George Gustav. "Domain decomposition and high order discretization of elliptic partial differential equations." Diss., Virginia Tech, 1994. http://hdl.handle.net/10919/39143.

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20

Pitts, George G. "Domain decomposition and high order discretization of elliptic partial differential equations." Diss., Virginia Tech, 1994. http://hdl.handle.net/10919/39143.

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Анотація:

Numerical solutions of partial differential equations (PDEs) resulting from problems in both the engineering and natural sciences result in solving large sparse linear systems Au = b. The construction of such linear systems and their solutions using either direct or iterative methods are topics of continuing research. The recent advent of parallel computer architectures has resulted in a search for good parallel algorithms to solve such systems, which in turn has led to a recent burgeoning of research into domain decomposition algorithms. Domain decomposition is a procedure which employs subdi

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21

Sweet, Erik. "ANALYTICAL AND NUMERICAL SOLUTIONS OF DIFFERENTIALEQUATIONS ARISING IN FLUID FLOW AND HEAT TRANSFER PROBLEMS." Doctoral diss., University of Central Florida, 2009. http://digital.library.ucf.edu/cdm/ref/collection/ETD/id/2585.

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The solutions of nonlinear ordinary or partial differential equations are important in the study of fluid flow and heat transfer. In this thesis we apply the Homotopy Analysis Method (HAM) and obtain solutions for several fluid flow and heat transfer problems. In chapter 1, a brief introduction to the history of homotopies and embeddings, along with some examples, are given. The application of homotopies and an introduction to the solutions procedure of differential equations (used in the thesis) are provided. In the chapters that follow, we apply HAM to a variety of problems to highlight its

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22

Macias, Diaz Jorge. "A Numerical Method for Computing Radially Symmetric Solutions of a Dissipative Nonlinear Modified Klein-Gordon Equation." ScholarWorks@UNO, 2004. http://scholarworks.uno.edu/td/167.

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In this paper we develop a finite-difference scheme to approximate radially symmetric solutions of a dissipative nonlinear modified Klein-Gordon equation in an open sphere around the origin, with constant internal and external damping coefficients and nonlinear term of the form G' (w) = w ^p, with p an odd number greater than 1. We prove that our scheme is consistent of quadratic order, and provide a necessary condition for it to be stable order n. Part of our study will be devoted to study the effects of internal and external damping.

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23

Trojan, Alice von. "Finite difference methods for advection and diffusion." Title page, abstract and contents only, 2001. http://web4.library.adelaide.edu.au/theses/09PH/09phv948.pdf.

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Анотація:

Includes bibliographical references (leaves 158-163). Concerns the development of high-order finite-difference methods on a uniform rectangular grid for advection and diffuse problems with smooth variable coefficients. This technique has been successfully applied to variable-coefficient advection and diffusion problems. Demonstrates that the new schemes may readily be incorporated into multi-dimensional problems by using locally one-dimensional techniques, or that they may be used in process splitting algorithms to solve complicatef time-dependent partial differential equations.

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24

Gyurko, Lajos Gergely. "Numerical methods for approximating solutions to rough differential equations." Thesis, University of Oxford, 2008. http://ora.ox.ac.uk/objects/uuid:d977be17-76c6-46d6-8691-6d3b7bd51f7a.

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The main motivation behind writing this thesis was to construct numerical methods to approximate solutions to differential equations driven by rough paths, where the solution is considered in the rough path-sense. Rough paths of inhomogeneous degree of smoothness as driving noise are considered. We also aimed to find applications of these numerical methods to stochastic differential equations. After sketching the core ideas of the Rough Paths Theory in Chapter 1, the versions of the core theorems corresponding to the inhomogeneous degree of smoothness case are stated and proved in Chapter 2 al

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25

Chen, Meng. "Intrinsic meshless methods for PDEs on manifolds and applications." HKBU Institutional Repository, 2018. https://repository.hkbu.edu.hk/etd_oa/528.

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Анотація:

Radial basis function (RBF) methods for partial differential equations (PDEs), either in bulk domains, on surfaces, or in a combination of the formers, arise in a wide range of practical applications. This thesis proposes numerical approaches of RBF-based meshless techniques to solve these three kinds of PDEs on stationary and nonstationary surfaces and domains. In Chapter 1, we introduce the background of RBF methods, some basic concepts, and error estimates for RBF interpolation. We then provide some preliminaries for manifolds, restricted RBFs on manifolds, and some convergence properties o

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26

Rebaza-Vasquez, Jorge. "Computation and continuation of equilibrium-to-periodic and periodic-to-periodic connections." Diss., Georgia Institute of Technology, 2002. http://hdl.handle.net/1853/28991.

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27

Shu, Yupeng. "Numerical Solutions of Generalized Burgers' Equations for Some Incompressible Non-Newtonian Fluids." ScholarWorks@UNO, 2015. http://scholarworks.uno.edu/td/2051.

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The author presents some generalized Burgers' equations for incompressible and isothermal flow of viscous non-Newtonian fluids based on the Cross model, the Carreau model, and the Power-Law model and some simple assumptions on the flows. The author numerically solves the traveling wave equations for the Cross model, the Carreau model, the Power-Law model by using industrial data. The author proves existence and uniqueness of solutions to the traveling wave equations of each of the three models. The author also provides numerical estimates of the shock thickness as well as maximum strain $\vare

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28

Bénézet, Cyril. "Study of numerical methods for partial hedging and switching problems with costs uncertainty." Thesis, Université de Paris (2019-....), 2019. http://www.theses.fr/2019UNIP7079.

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Nous apportons dans cette thèse quelques contributions à l’étude théorique et numérique de certains problèmes de contrôle stochastique, ainsi que leurs applications aux mathématiques financières et à la gestion des risques financiers. Ces applications portent sur des problématiques de valorisation et de couverture faibles de produits financiers, ainsi que sur des problématiques réglementaires. Nous proposons des méthodes numériques afin de calculer efficacement ces quantités pour lesquelles il n’existe pas de formule explicite. Enfin, nous étudions les équations différentielles stochastiques r

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29

Li, Wen. "Numerical methods for the solution of the HJB equations arising in European and American option pricing with proportional transaction costs." University of Western Australia. School of Mathematics and Statistics, 2010. http://theses.library.uwa.edu.au/adt-WU2010.0098.

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This thesis is concerned with the investigation of numerical methods for the solution of the Hamilton-Jacobi-Bellman (HJB) equations arising in European and American option pricing with proportional transaction costs. We first consider the problem of computing reservation purchase and write prices of a European option in the model proposed by Davis, Panas and Zariphopoulou [19]. It has been shown [19] that computing the reservation purchase and write prices of a European option involves solving three different fully nonlinear HJB equations. In this thesis, we propose a penalty approach combine

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30

Maroofi, Hamed. "Applications of the Monge - Kantorovich theory." Diss., Georgia Institute of Technology, 2002. http://hdl.handle.net/1853/29197.

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31

Moita, Daniel. "Desempenho de esquemas numéricos na modelagem da não linearidade da precipitação em um modelo atmosférico simplificado." Laboratório Nacional de Computação científica, 2011. https://tede.lncc.br/handle/tede/159.

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Анотація:

Made available in DSpace on 2015-03-04T18:57:49Z (GMT). No. of bitstreams: 1 danielmoita_tesefinal.pdf: 1307742 bytes, checksum: 19f5820728d061b2b71cf62a0ffd0433 (MD5) Previous issue date: 2011-04-27<br>The interaction between large-scale ux fields and precipitation fields in the tropical atmosphere can produce sharp boundaries between dry and humid regions (limited ahead by the rainfall front). As the speed of propagation of disturbances in these regions are di_erent, they form a discontinuity (Days and Pauluis, 2009). This phenomenon can be represented by a system of equations formed by

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32

Li, Hongwei. "Local absorbing boundary conditions for wave propagations." HKBU Institutional Repository, 2012. https://repository.hkbu.edu.hk/etd_ra/1434.

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33

Mohd, Damanhuri Nor Alisa. "The numerical approximation to solutions for the double-slip and double-spin model for the deformation and flow of granular materials." Thesis, University of Manchester, 2017. https://www.research.manchester.ac.uk/portal/en/theses/the-numerical-approximation-to-solutions-for-the-doubleslip-and-doublespin-model-for-the-deformation-and-flow-of-granular-materials(9986ac45-e48c-4061-a299-a80b2e665c3e).html.

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The aim of this thesis is to develop a numerical method to find approximations to solutions of the double-slip and double-spin model for the deformation and flow of granular materials. The model incorporates the physical and kinematic concepts of yield, shearing motion on slip lines, dilatation and average grain rotation. The equations governing the model comprise a set of five first order partial differential equations for the five dependent variables comprising two stress variables, two velocity components and the density. For steady state flows, the model is hyperbolic and the characteristi

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34

Figueroa, Leonardo E. "Deterministic simulation of multi-beaded models of dilute polymer solutions." Thesis, University of Oxford, 2011. http://ora.ox.ac.uk/objects/uuid:4c3414ba-415a-4109-8e98-6c4fa24f9cdc.

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We study the convergence of a nonlinear approximation method introduced in the engineering literature for the numerical solution of a high-dimensional Fokker--Planck equation featuring in Navier--Stokes--Fokker--Planck systems that arise in kinetic models of dilute polymers. To do so, we build on the analysis carried out recently by Le~Bris, Leli\`evre and Maday (Const. Approx. 30: 621--651, 2009) in the case of Poisson's equation on a rectangular domain in $\mathbb{R}^2$, subject to a homogeneous Dirichlet boundary condition, where they exploited the connection of the approximation method wit

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35

Al, Zohbi Maryam. "Contributions to the existence, uniqueness, and contraction of the solutions to some evolutionary partial differential equations." Thesis, Compiègne, 2021. http://www.theses.fr/2021COMP2646.

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Dans cette thèse, nous nous sommes principalement intéressés à l’étude théorique et numérique de quelques équations qui décrivent la dynamique des densités des dislocations. Les dislocations sont des défauts microscopiques qui se déplacent dans les matériaux sous l’effet des contraintes extérieures. Dans un premier travail, nous démontrons un résultat d’existence globale en temps des solutions discontinues pour un système hyperbolique diagonal qui n’est pas nécessairement strictement hyperbolique, dans un espace unidimensionnel. Ainsi dans un deuxième travail, nous élargissons notre portée en

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36

Martel, Sofiane. "Theoretical and numerical analysis of invariant measures of viscous stochastic scalar conservation laws." Thesis, Paris Est, 2019. http://www.theses.fr/2019PESC1040.

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Cette thèse se consacre à une analyse théorique puis numérique d'une certaine classe d'équations aux dérivées partielles stochastiques (EDPS) : les lois de conservation scalaires avec viscosité et avec un forçage aléatoire de type additif et bruit blanc en temps. Un exemple typique est l'équation de Burgers stochastique, motivée par la théorie de la turbulence. On s'intéresse particulièrement au comportement en temps long des solutions de ces équations à travers une étude des mesures invariantes. La partie théorique de la thèse constitue le chapitre 2. Dans ce chapitre, on prouve l'existence e

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37

McCoy, James A. (James Alexander) 1976. "The surface area preserving mean curvature flow." Monash University, Dept. of Mathematics, 2002. http://arrow.monash.edu.au/hdl/1959.1/8291.

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38

Brubaker, Lauren P. "Completely Residual Based Code Verification." University of Akron / OhioLINK, 2006. http://rave.ohiolink.edu/etdc/view?acc_num=akron1132592325.

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39

Bréhier, Charles-Edouard. "Numerical analysis of highly oscillatory Stochastic PDEs." Phd thesis, École normale supérieure de Cachan - ENS Cachan, 2012. http://tel.archives-ouvertes.fr/tel-00824693.

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In a first part, we are interested in the behavior of a system of Stochastic PDEs with two time-scales- more precisely, we focus on the approximation of the slow component thanks to an efficient numerical scheme. We first prove an averaging principle, which states that the slow component converges to the solution of the so-called averaged equation. We then show that a numerical scheme of Euler type provides a good approximation of an unknown coefficient appearing in the averaged equation. Finally, we build and we analyze a discretization scheme based on the previous results, according to the H

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40

Paillere, Henri J. "Multidimensional upwind residual distribution schemes for the Euler and Navier-Stokes equations on unstructured grids." Doctoral thesis, Universite Libre de Bruxelles, 1995. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/212553.

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<p align="justify">Une approche multidimensionelle pour la résolution numérique des équations d'Euler et de Navier-Stokes sur maillages non-structurés est proposée. Dans une première partie, un exposé complet des schémas de distribution, dits de "fluctuation-splitting" ,est décrit, comprenant une étude comparative des schémas décentrés, positifs et de 2ème ordre, pour résoudre l'équation de convection à coefficients constants, ainsi qu'une étude théorique et numérique de la précision des schémas sur maillages réguliers et distordus. L'extension à des lois de conservation non-linéaires est auss

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41

Coimbra, Tiago Antonio Alves 1981. "Solução da equação da onda imagem para continuação do afastamento mediante o metodo das caracteristicas." [s.n.], 2010. http://repositorio.unicamp.br/jspui/handle/REPOSIP/306030.

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Orientadores: Maria Amelia Novais Schleicher, Joerg Dietrich Wilhelm Schleicher<br>Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica<br>Made available in DSpace on 2018-08-15T16:25:22Z (GMT). No. of bitstreams: 1 Coimbra_TiagoAntonioAlves_M.pdf: 1644714 bytes, checksum: 5d506a3202c2283333d0f29819623fcc (MD5) Previous issue date: 2010<br>Resumo: O deslocamento de um evento sísmico sob a chamada operação de continuação de afastamento (Offset Continuation Operation - OCO) pode ser descrita por uma equação diferencial parcial

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42

Lao, Kun Leng. "Multigrid algorithm based on cyclic reduction for convection diffusion equations." Thesis, University of Macau, 2010. http://umaclib3.umac.mo/record=b2148274.

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43

Landry, Richard S. Jr. "An Application of M-matrices to Preserve Bounded Positive Solutions to the Evolution Equations of Biofilm Models." ScholarWorks@UNO, 2017. https://scholarworks.uno.edu/td/2418.

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In this work, we design a linear, two step implicit finite difference method to approximate the solutions of a biological system that describes the interaction between a microbial colony and a surrounding substrate. Three separate models are analyzed, all of which can be described as systems of partial differential equations (PDE)s with nonlinear diffusion and reaction, where the biological colony grows and decays based on the substrate bioavailability. The systems under investigation are all complex models describing the dynamics of biological films. In view of the difficulties to calculate a

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44

Pinheiro, Nathalie Carvalho. "Controle impulsional limitação da variação de nivel com minimização das atuações." [s.n.], 2009. http://repositorio.unicamp.br/jspui/handle/REPOSIP/259269.

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Orientador: João Bosco Ribeiro do Val<br>Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Eletrica e de Computação<br>Made available in DSpace on 2018-08-14T11:15:46Z (GMT). No. of bitstreams: 1 Pinheiro_NathalieCarvalho_M.pdf: 2872807 bytes, checksum: 929137a3cc76534c1832b041f3175ff3 (MD5) Previous issue date: 2009<br>Resumo: Os elevados custos de produção na extração de petróleo marítimo são reduzidos com um sistema inovador que a Petrobras está desenvolvendo, denominado VASPS (do inglês, Vertical Annular Separation and Pumping System), capaz de separar g

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45

Williamson, Rosemary Anne. "Numerical solution of hyperbolic partial differential equations." Thesis, University of Cambridge, 1985. https://www.repository.cam.ac.uk/handle/1810/278503.

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46

Cardoso, André da Silva. "DFLD-EXP: uma solução semi-analítica para a equação de advecção-dispersão." Universidade do Estado do Rio de Janeiro, 2008. http://www.bdtd.uerj.br/tde_busca/arquivo.php?codArquivo=771.

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A equação de advecção-dispersão possui grande importância na engenharia e nas ciências aplicadas. No entanto, como é bem conhecido, a obtenção de uma solução numérica apropriada para essa equação é um problema desafiador tanto para engenheiros como para matemáticos, físicos e outros profissionais que trabalham com a modelagem de fenômenos associados a ela. Muitos métodos numéricos desenvolvidos podem apresentar uma série de inconvenientes, tais como oscilações, dispersão e/ou dissipação numérica e instabilidade, além de serem inapropriados para determinadas condições de contorno. O presente tr

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47

Morris, Graham Peter. "Parameter recovery in AC solution-phase voltammetry and a consideration of some issues arising when applied to surface-confined reactions." Thesis, University of Oxford, 2014. http://ora.ox.ac.uk/objects/uuid:1b1d40f3-ef1a-4f64-b500-17ce34630c43.

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A major problem in the quantitative analysis of AC voltammetric data has been the variance in results between laboratories, often resulting from a reliance on "heuristic" methods of parameter estimation that are strongly dependent on the choices of the operator. In this thesis, an automatic method for parameter estimation will be tested in the context of experiments involving electron-transfer processes in solution-phase. It will be shown that this automatic method produces parameter estimates consistent with those from other methods and the literature in the case of the ferri-/ferrocyanide co

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48

Tråsdahl, Øystein. "Numerical solution of partial differential equations in time-dependent domains." Thesis, Norwegian University of Science and Technology, Department of Mathematical Sciences, 2008. http://urn.kb.se/resolve?urn=urn:nbn:no:ntnu:diva-9752.

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<p>Numerical solution of heat transfer and fluid flow problems in two spatial dimensions is studied. An arbitrary Lagrangian-Eulerian (ALE) formulation of the governing equations is applied to handle time-dependent geometries. A Legendre spectral method is used for the spatial discretization, and the temporal discretization is done with a semi-implicit multi-step method. The Stefan problem, a convection-diffusion boundary value problem modeling phase transition, makes for some interesting model problems. One problem is solved numerically to obtain first, second and third order convergence in t

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Ibrahem, Abdul Nabi Ismail. "The numerical solution of partial differential equations on unbounded domains." Thesis, Keele University, 1989. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.279648.

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Pun, K. S. "The numerical solution of partial differential equations with the Tau method." Thesis, Imperial College London, 1985. http://hdl.handle.net/10044/1/37823.

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