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Dissertations / Theses on the topic 'Heat equation Numerical solutions'

Author: Grafiati

Published: 4 June 2021

Last updated: 13 February 2022

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1

Hayman, Kenneth John. "Finite-difference methods for the diffusion equation." Title page, table of contents and summary only, 1988. http://web4.library.adelaide.edu.au/theses/09PH/09phh422.pdf.

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2

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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3

Sweet, Erik. "Analytical and numerical solutions of differential equations arising in fluid flow and heat transfer problems." Orlando, Fla. : University of Central Florida, 2009. http://purl.fcla.edu/fcla/etd/CFE0002889.

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4

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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5

Al-Jawary, Majeed Ahmed Weli. "The radial integration boundary integral and integro-differential equation methods for numerical solution of problems with variable coefficients." Thesis, Brunel University, 2012. http://bura.brunel.ac.uk/handle/2438/6449.

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The boundary element method (BEM) has become a powerful method for the numerical solution of boundary-value problems (BVPs), due to its ability (at least for problems with constant coefficients) of reducing a BVP for a linear partial differential equation (PDE) defined in a domain to an integral equation defined on the boundary, leading to a simplified discretisation process with boundary elements only. On the other hand, the coefficients in the mathematical model of a physical problem typically correspond to the material parameters of the problem. In many physical problems, the governing equa

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6

Ferreira, Fábio Freitas. "Problemas inversos sobre a esfera." Universidade do Estado do Rio de Janeiro, 2008. http://www.bdtd.uerj.br/tde_busca/arquivo.php?codArquivo=889.

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Fundação Carlos Chagas Filho de Amparo a Pesquisa do Estado do Rio de Janeiro<br>O objetivo desta tese é o desenvolvimento de algoritmos para determinar as soluções, e para determinação de fontes, das equações de Poisson e da condução de calor definidas em uma esfera. Determinamos as formas das equações de Poisson e de calor sobre a esfera, e desenvolvemos métodos iterativos, baseados em uma malha icosaedral e sua respectiva malha dual, para obter as soluções das mesmas. Mostramos que os métodos iterativos convergem para as soluções das equações discretizadas. Empregamos o método de regulariza

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7

Simmel, Martin. "Two numerical solutions for the stochastic collection equation." Universitätsbibliothek Leipzig, 2016. http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-215378.

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Two different methods are used to solve the stochastic collection equation (SCE) numerically. They are called linear discrete method (LDM) and bin shift method (BSM), respectively. Conceptually, both of them are similar to the well-known discrete method (DM) of Kovetz and Olund. For LDM and BSM, their concept is extended to two prognostic moments. Therefore, the \"splitting factors\" (which are constant in time for DM) become time-dependent for LDM and BSM. Simulations are shown for the Golovin kernel (for which an analytical solution is available) and the hydrodynamic kernel after Hall. Diffe

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8

Simmel, Martin. "Two numerical solutions for the stochastic collection equation." Wissenschaftliche Mitteilungen des Leipziger Instituts für Meteorologie ; 17 = Meteorologische Arbeiten aus Leipzig ; 5 (2000), S. 61-73, 2000. https://ul.qucosa.de/id/qucosa%3A15149.

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Two different methods are used to solve the stochastic collection equation (SCE) numerically. They are called linear discrete method (LDM) and bin shift method (BSM), respectively. Conceptually, both of them are similar to the well-known discrete method (DM) of Kovetz and Olund. For LDM and BSM, their concept is extended to two prognostic moments. Therefore, the \"splitting factors\" (which are constant in time for DM) become time-dependent for LDM and BSM. Simulations are shown for the Golovin kernel (for which an analytical solution is available) and the hydrodynamic kernel after Hall. Diffe

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9

Sjölander, Filip. "Numerical solutions to the Boussinesq equation and the Korteweg-de Vries equation." Thesis, KTH, Skolan för teknikvetenskap (SCI), 2021. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-297544.

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The aim of the report is to numerically construct solutions to two analytically solvable non-linear differential equations: the Korteweg–De Vries equation and the Boussinesq equation. To accomplish this, a range of numerical methods where implemented, including Galerkin methods. To asses the accuracy of the solutions, analytic solutions were derived for reference. Characteristic of both equations is that they support a certain type of wave-solutions called "soliton solutions", which admit an intuitive physical interpretation as solitary traveling waves. Theses solutions are the ones simulated.

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10

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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11

Scheid, Jean-François. "Étude théorique et numérique de l'évolution morphologique d'interfaces." Paris 11, 1994. http://www.theses.fr/1994PA112027.

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L'objet de cette thèse est d'étudier un processus de dissolution-croissance où une phase solide est en contact avec une phase liquide. Ce phénomène s'accompagne d'un changement de géométrie de l'interface entre ces deux phases. Les lois physiques qui gouvernent ce processus conduisent mathématiquement à une loi de déplacement pour l'interface où la courbure moyenne apparait de façon non linéaire et à une équation parabolique pour la concentration de l'espèce chimique passée en solution. Il s'agit d'un problème de Stefan avec tension superficielle en dimension deux d'espace. Au chapitre 1, nous

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12

Duthil, Eric Patxi. "Thermoacoustic heat pumping study : experimental and numerical approaches /." View Abstract or Full-Text, 2003. http://library.ust.hk/cgi/db/thesis.pl?MECH%202003%20DUTHIL.

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Thesis (Ph. D.)--Hong Kong University of Science and Technology, 2003.<br>Includes bibliographical references (leaves 122-129). Also available in electronic version. Access restricted to campus users.

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13

Wilkinson, Rebecca L. "Numerical explorations of cake baking using the nonlinear heat equation." View electronic thesis, 2008. http://dl.uncw.edu/etd/2008-1/wilkinsonr/rebeccawilkinson.pdf.

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14

Sundström, Carl. "Numerical solutions to high frequency approximations of the scalar wave equation." Thesis, Uppsala universitet, Tillämpad beräkningsvetenskap, 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-429072.

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Throughout many fields of science and engineering, the need for describing waveequations is crucial. Solving the wave equation for high-frequency waves istime-consuming, requires a fine mesh size and memory usage. The main goal wasimplementing and comparing different solution methods for high-frequency waves.Four different methods have been implemented and compared in terms of runtimeand discretization error. From my results, the method which performs the best is thefast sweeping method. For the fast marching method, the time-complexity of thenumerical solver was higher than expected which ind

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15

Van, Cong Tuan Son. "Numerical solutions to some inverse problems." Diss., Kansas State University, 2017. http://hdl.handle.net/2097/38248.

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Doctor of Philosophy<br>Department of Mathematics<br>Alexander G. Ramm<br>In this dissertation, the author presents two independent researches on inverse problems: (1) creating materials in which heat propagates a long a line and (2) 3D inverse scattering problem with non-over-determined data. The theories of these methods were developed by Professor Alexander Ramm and are presented in Chapters 1 and 3. The algorithms and numerical results are taken from the papers of Professor Alexander Ramm and the author and are presented in Chapters 2 and 4.

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16

Tzanetis, Dimitrios E. "Global existence and asymptotic behaviour of unbounded solutions for the semilinear heat equation." Thesis, Heriot-Watt University, 1986. http://hdl.handle.net/10399/1604.

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17

Pusch, Gordon D. "Differential algebraic methods for obtaining approximate numerical solutions to the Hamilton-Jacobi equation." Diss., This resource online, 1990. http://scholar.lib.vt.edu/theses/available/etd-07282008-135711/.

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18

Agiza, Hamdy N. "A numerical and theoretical study of solutions to a damped nonlinear wave equation." Thesis, Heriot-Watt University, 1987. http://hdl.handle.net/10399/1058.

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19

Sagheer, Muhammad. "Mathematical analysis and numerical solutions of an integral equation arising from population dynamics." Thesis, University of Sussex, 2005. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.420495.

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20

Chiang, Shihchung. "Numerical solutions for a class of singular integrodifferential equations." Diss., This resource online, 1996. http://scholar.lib.vt.edu/theses/available/etd-06062008-151231/.

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21

Huang, Jeffrey. "Numerical solutions of continuous wave beam in nonlinear media." PDXScholar, 1987. https://pdxscholar.library.pdx.edu/open_access_etds/3742.

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Deformation of a Gaussian beam is observed when it propagates through a plasma. Self-focusing of the beam may be observed when the intensity of the laser increases the index of refraction of plasma gas. Due to the difficulties in solving the nonlinear partial differential equation in Maxwell's wave equation, a numerical technique has been developed in favor of the traditional analytical method. Result of numerical solution shows consistency with the analytical method. This further suggests the validity of the numerical technique employed. A three dimensional graphics package was used to depict

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22

Antoniouk, Alexandra, Oleg Kiselev, Vitaly Stepanenko, and Nikolai Tarkhanov. "Asymptotic solutions of the Dirichlet problem for the heat equation at a characteristic point." Universität Potsdam, 2012. http://opus.kobv.de/ubp/volltexte/2012/6198/.

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The Dirichlet problem for the heat equation in a bounded domain is characteristic, for there are boundary points at which the boundary touches a characteristic hyperplane t = c, c being a constant. It was I.G. Petrovskii (1934) who first found necessary and sufficient conditions on the boundary which guarantee that the solution is continuous up to the characteristic point, provided that the Dirichlet data are continuous. This paper initiated standing interest in studying general boundary value problems for parabolic equations in bounded domains. We contribute to the study by constructing a for

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23

Hårderup, Peder, and William Brorsson. "A Numerical and Analytical Investigation of The sine-Gordon Equation and Its Soliton Solutions." Thesis, KTH, Skolan för teknikvetenskap (SCI), 2021. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-297564.

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This thesis investigates the nonlinear partial differential equation known as sine-Gordon and its special soliton solutions.Simpler analytical results are derived and more advanced methods and their results are discussed.Further, a finite difference scheme is derived, implemented and compared against a known energy conserving scheme of sine-Gordon in terms of stability, accuracy, convergence and computation time.The complete solvability of the equation enables comparison between numerical solutions and their analytical counterparts.No unified answer to which numerical scheme is best was determ

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24

Porter, Annabelle Louise. "The evolution of equation-solving: Linear, quadratic, and cubic." CSUSB ScholarWorks, 2006. https://scholarworks.lib.csusb.edu/etd-project/3069.

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This paper is intended as a professional developmental tool to help secondary algebra teachers understand the concepts underlying the algorithms we use, how these algorithms developed, and why they work. It uses a historical perspective to highlight many of the concepts underlying modern equation solving.

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25

Yevik, Andrei. "Numerical approximations to the stationary solutions of stochastic differential equations." Thesis, Loughborough University, 2011. https://dspace.lboro.ac.uk/2134/7777.

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This thesis investigates the possibility of approximating stationary solutions of stochastic differential equations using numerical methods. We consider a particular class of stochastic differential equations, which are known to generate random dynamical systems. The existence of stochastic stationary solution is proved using global attractor approach. Euler's numerical method, applied to the stochastic differential equation, is proved to generate a discrete random dynamical system. The existence of stationary solution is proved again using global attractor approach. At last we prove that the

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26

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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27

Weiß, Jan-Philipp. "Numerical analysis of lattice Boltzmann methods for the heat equation on a bounded interval." Karlsruhe : Univ.-Verl. Karlsruhe, 2006. http://www.uvka.de/univerlag/volltexte/2006/179/.

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28

Zheng, Bing. "Incorporating equation solving into unification through stratified term rewriting." Thesis, Virginia Polytechnic Institute and State University, 1989. http://hdl.handle.net/10919/52096.

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This thesis studies equational theories incorporated into unification and describes STAR, a stratified term rewriting system that achieves a full integration. STAR is an advance over existing systems because it integrates an equational theory with unification at a lower, more fundamental level. Certain properties of STAR are proven including termination and confluence. We also discuss the algorithmic complexity of the reduction algorithm, a vital component of STAR. We compare our system with narrowing and discuss the merits and drawbacks of each technique. Since our system is an experimental

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29

Al-Hussyni, Saad Kohel Ali. "Numerical study of turbulent plane jets in still and flowing environments employing two-equation k-ε model". Thesis, University of Edinburgh, 1987. http://hdl.handle.net/1842/11065.

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30

Volkin, Robert P. "Spherical Shell Solutions to the Radially Symmetric Aggregation Equation: Analysis and a Novel Numerical Method." Case Western Reserve University School of Graduate Studies / OhioLINK, 2020. http://rave.ohiolink.edu/etdc/view?acc_num=case1575639958498416.

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31

Tyler, Jonathan. "Analysis and implementation of high-order compact finite difference schemes /." Diss., CLICK HERE for online access, 2007. http://contentdm.lib.byu.edu/ETD/image/etd2177.pdf.

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32

Koutoumbas, Anastasios M. "Bidirectional and unidirectional spectral representations for the scalar wave equation." Thesis, Virginia Tech, 1990. http://hdl.handle.net/10919/41904.

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<p>The Cauchy problem associated with the scalar wave equation in free space is used as a vehicle for a critical examination and assessment of the bidirectional and unidirectional spectral representations. These two novel methods for synthesizing wave signals are distinct from the superposition principle underlying the conventional Fourier method and they can effectively be used to derive a large class of localized solutions to the scalar wave equation. The bidirectional spectral representation is presented as an extension of Brittingham's ansatz and Ziolkowski's Focus Wave Mode spectral repre

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33

Dubois, Olivier 1980. "Optimized Schwarz methods for the advection-diffusion equation and for problems with discontinuous coefficients." Thesis, McGill University, 2007. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=103379.

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Optimized Schwarz methods are iterative domain decomposition procedures with greatly improved convergence properties, for solving second order elliptic boundary value problems. The enhanced convergence is obtained by replacing the Dirichlet transmission conditions in the classical Schwarz iteration with more general conditions that are optimized for performance. The convergence is optimized through the solution of a min-max problem. The theoretical study of the min-max problems gives explicit formulas or characterizations for the optimized transmission conditions for practical use, and it perm

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34

Liu, Fang-Lan. "Some asymptotic stability results for the Boussinesq equation." Diss., Virginia Tech, 1993. http://hdl.handle.net/10919/40052.

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35

Jonsson, Tobias. "On the one dimensional Stefan problem : with some numerical analysis." Thesis, Umeå universitet, Institutionen för matematik och matematisk statistik, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-80215.

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In this thesis we present the Stefan problem with two boundary conditions, one constant and one time-dependent. This problem is a classic example of a free boundary problem in partial differential equations, with a free boundary moving in time. Some properties are being proved for the one-dimensional case and the important Stefan condition is also derived. The importance of the maximum principle, and the existence of a unique solution are being discussed. To numerically solve this problem, an analysis when the time t goes to zero is being done. The approximative solutions are shown graphically

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36

Knaub, Karl R. "On the asymptotic behavior of internal layer solutions of advection-diffusion-reaction equations /." Thesis, Connect to this title online; UW restricted, 2001. http://hdl.handle.net/1773/6772.

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37

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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38

Kurianski, Kristin Marie-Dettmers. "Estimates for solutions to the Dysthe equation and numerical simulations of walking droplets in harmonic potentials." Thesis, Massachusetts Institute of Technology, 2019. https://hdl.handle.net/1721.1/122173.

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Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2019<br>Cataloged from PDF version of thesis.<br>Includes bibliographical references (pages 119-124).<br>In this thesis, we study wave-type phenomena both from a numerical point of view and a theoretical one. We first present the results of a numerical investigation of droplets walking in a harmonic potential on a vibrating fluid bath. The droplet's trajectory is described by an integro-differential equation, which is simulated numerically in various parameter regimes. We produce a regime diagram that summarizes

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39

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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40

Liu, Guanhui, and 刘冠辉. "Formulation of multifield finite element models for Helmholtzproblems." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2010. http://hub.hku.hk/bib/B44204875.

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41

Ploskic, Adnan. "Technical solutions for low-temperature heat emission in buildings." Doctoral thesis, KTH, Strömnings- och klimatteknik, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-133221.

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The European Union is planning to greatly decrease energy consumption during the coming decades. The ultimate goal is to create sustainable communities that are energy neutral. One way of achieving this challenging goal may be to use efficient hydronic (water-based) heating systems supported by heat pumps. The main objective of the research reported in this work was to improve the thermal performance of wall-mounted hydronic space heaters (radiators). By improving the thermal efficiency of the radiators, their operating temperatures can be lowered without decreasing their thermal outputs. This

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42

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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43

Fok, Chin Man. "Numerical solutions for the Navier-Stokes equations and the Fokker-Planck equations using spectral methods." HKBU Institutional Repository, 2002. http://repository.hkbu.edu.hk/etd_ra/435.

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44

Lampshire, Gregory B. "Review of random media homogenization using effective medium theories." Thesis, Virginia Tech, 1992. http://hdl.handle.net/10919/40659.

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<p>Calculation of propagation constants in particulate matter is an important aspect of wave propagation analysis in engineering disciplines such as satellite comnlunication, geophysical exploration, radio astronomy and material science. It is important to understand why different propagation constants produced by different theories are not applicable to a particular problem. Homogenization of the random media using effective medium theories yields the effective propagation constants by effacing the particulate, microscopic nature of the medium. The Maxwell-Gamet and Bruggeman effective medium

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45

Weiß, Jan-Philipp [Verfasser]. "Numerical analysis of Lattice Boltzmann methods for the heat equation on a bounded interval / von Jan Philipp Weiß." Karlsruhe : Univ.-Verl. Karlsruhe, 2006. http://d-nb.info/982595697/34.

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46

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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47

Tyler, Jonathan G. "Analysis and Implementation of High-Order Compact Finite Difference Schemes." BYU ScholarsArchive, 2007. https://scholarsarchive.byu.edu/etd/1278.

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The derivation of centered compact schemes at interior and boundary grid points is performed and an analysis of stability and computational efficiency is given. Compact schemes are high order implicit methods for numerical solutions of initial and/or boundary value problems modeled by differential equations. These schemes generally require smaller stencils than the traditional explicit finite difference counterparts. To avoid numerical instabilities at and near boundaries and in regions of mesh non-uniformity, a numerical filtering technique is employed. Experiments for non-stationary linear p

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48

Domeij, Bäckryd Rebecka. "Simulation of Heat Transfer on a Gas Sensor Component." Thesis, Linköping University, Department of Mathematics, 2005. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-131.

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<p>Gas sensors are today used in many different application areas, and one growing future market is battery operated sensors. As many gas sensor components are heated, one major limit of the operation time is caused by the power dissipated as heat. AppliedSensor is a company that develops and produces gas sensor components, modules and solutions, among which battery operated gas sensors are one targeted market.</p><p>The aim of the diploma work has been to simulate the heat transfer on a hydrogen gas sensor component and its closest surroundings consisting of a carrier mounted on a printed cir

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49

Liu, Bing. "Properties Model for Aqueous Sodium Chloride Solutions near the Critical Point of Water." Diss., CLICK HERE for online access, 2005. http://contentdm.lib.byu.edu/ETD/image/etd1034.pdf.

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50

Cortez, Manuel Fernando. "Explosion en temps fini de solutions d’équations dispersives ou dissipatives non-linéaires." Thesis, Lyon 1, 2015. http://www.theses.fr/2015LYO10198/document.

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Le sujet de cette thèse est la formation de singularités pour certaines équations d'évolution dispersives et/ou dissipatives non-linéaires. Notre travail est axé sur les problèmes de Cauchy, généralement avec des conditions aux limites périodiques ou dans tout $\mathbb{R}^n$. Notre objectif est de fournir les conditions nécessaires ou suffisantes (ou les deux) sur les données initiales $u_0(x)$, garantissant que la durée de vie $T^{*}$ de la solution résultant de $u_0$ est finie ou non. Nous étudions deux types d'équations : une équation parabolique non linéaires et une classe d'équations d'on

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