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The application of the multigrid algorithm to the solution of stiff ordinary differential equations resulting from partial differential equations.Parumasur, Nabendra. January 1992 (has links)
We wish to apply the newly developed multigrid method [14] to the solution of
ODEs resulting from the semi-discretization of time dependent PDEs by the
method of lines. In particular, we consider the general form of two important
PDE equations occuring in practice, viz. the nonlinear diffusion equation and
the telegraph equation. Furthermore, we briefly examine a practical area, viz.
atmospheric physics where we feel this method might be of significance. In
order to offer the method to a wider range of PC users we present a computer
program, called PDEMGS. The purpose of this program is to relieve the user
of much of the expensive and time consuming effort involved in the solution
of nonlinear PDEs. A wide variety of examples are given to demonstrate the
usefulness of the multigrid method and the versatility of PDEMGS. / Thesis (M.Sc.)-University of Natal, Durban, 1992.
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Estimation of parameters in partial differential equations with applications to petroleum reservoir description /Chen, Wen Hsiung. Seinfeld, John H., January 1974 (has links)
Thesis (Ph. D.). UM #74-17,941. / Title from document title page. Includes bibliographical references. Available in PDF format via the World Wide Web.
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Some innovative numerical approaches for pricing American optionsZhang, Jin. January 2007 (has links)
Thesis (M.Sc.-Res.)--University of Wollongong, 2007. / Typescript. Includes bibliographical references: leaf 77-80.
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Nonlinear convective instability of fronts a case study /Ghazaryan, Anna R., January 2005 (has links)
Thesis (Ph.D.)--Ohio State University, 2005. / Title from first page of PDF file. Document formatted into pages; contains ix, 176 p.; also includes graphics. Includes bibliographical references (p. 172-176). Available online via OhioLINK's ETD Center
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The method of moments solution of a nonconformal volume integral equation via the IE-FFT algorithm for electromagnetic scattering from penetrable objectsOzdemir, Nilufer A., January 2007 (has links)
Thesis (Ph. D.)--Ohio State University, 2007. / Title from first page of PDF file. Includes bibliographical references (p. 114-118).
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Latent relationships between Markov processes, semigroups and partial differential equationsKajama, Safari Mukeru 30 June 2008 (has links)
This research investigates existing relationships between the three apparently unrelated
subjects: Markov process, Semigroups and Partial difierential equations.
Markov processes define semigroups through their transition functions. Conversely
particular semigroups determine transition functions and can be regarded as Markov
processes. We have exploited these relationships to study some Markov chains.
The infnitesimal generator of a Feller semigroup on the closure of a bounded domain
of Rn; (n ^ 2), is an integro-diferential operator in the interior of the domain and verifes
a boundary condition.
The existence of a Feller semigroup defined by a diferential operator and a boundary
condition is due to the existence of solution of a bounded value problem. From this result
other existence suficient conditions on the existence of Feller semigroups have been
obtained and we have applied some of them to construct Feller semigroups on the unity
disk of R2. / Decision Sciences / M. Sc. (Operations Research)
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Solução da equação da onda imagem para continuação do afastamento mediante o metodo das caracteristicas / Solution of the image-wave equation for offset continuation by means of the methd of characteristicsCoimbra, Tiago Antonio Alves, 1981- 03 October 2010 (has links)
Orientadores: Maria Amelia Novais Schleicher, Joerg Dietrich Wilhelm Schleicher / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica / 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 / 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 de segunda ordem que foi denominada de equação da onda imagem para OCO. Por substituição de uma solução tentativa da forma da teoria dos raios, pode se deduzir uma equação iconal OCO que descreve os aspectos cinemáticos da propagação da onda imagem OCO. Neste trabalho, resolvemos a equação da onda imagem OCO por meio do método das características. As características desta equação são as trajetórias OCO que descrevem o caminho do deslocamento de um evento sísmico sob variação do afastamento entre fonte e receptor. O conjunto de pontos finais de diversas trajetórias OCO, traçadas a partir do mesmo afastamento inicial até o mesmo afastamento final, define o raio de velocidade OCO ou, mais breve, raio OCO. Este raio OCO pode ser empregado para análise de velocidade. O algoritmo consiste do traçamento de raios OCO e então encontrar o ponto de interseção entre o raio OCO e o evento de reflexão sísmica dentro da seção final de afastamento comum. O procedimento tem a vantagem sobre a análise de velocidade convencional de que está baseado numa comparação de dados simulados com dados adquiridos ao invés de dois conjuntos de dados simulados. Exemplos numéricos demonstram que o traçamento de raios OCO pode ser executado de maneira precisa e de que a análise de velocidade resultante fornece velocidades confiáveis. Além disso, baseado nas expressões analíticas para os raios OCO que começam a partir do afastamento zero (migraton to common offset - MCO), deduzimos uma equação da onda imagem para continuação de velocidade MCO. Demonstramos que, em muitas situações práticas, esta equação pode ser empregada diretamente para OCO, assim evitando a necessidade de traçar trajetórias e raios OCO / Abstract: The dislocation of a seismic event under the so-called Offset Continuation Operation (OCO) can be described by a second-order partial differential equation, which has been called the OCO image-wave equation. By substitution of a ray-like trial solution, an OCO image-wave eikonal equation is obtained that describes the kinematic aspects of OCO imagewave propagation. In this work, we solve the OCO image-wave eikonal equation by means of the method of characteristics. The characteristics of this equation are the OCO trajectories that describe the path of dislocation of a seismic event under variation of the source-receiver offset. The set of endpoints of several OCO trajectories traced from the same initial to the same final offset under varying values for the medium velocity defines the OCO velocity ray or briefly OCO ray. This OCO ray can be employed for velocity analysis. The algorithm consists of OCO ray tracing an then finding the intersection point of the OCO ray with the seismic reflection event in the final common-offset section. The procedure has the advantage over conventional velocity analysis that it is based on a comparison of simulated and acquired data rather than two sets of simulated data. Numerical examples demonstrate that the OCO ray tracing can be accurately executed and that the resulting velocity analysis yields reliable velocities. Moreover, based on the analytic expressions for the OCO rays starting from zero-offset (migraton to common offset, MCO), we derived an image-wave equation for MCO velocity continuation. We demonstrate that in many practical situations this equation can be directly employed for OCO, thus avoiding the need to trace OCO trajectories and OCO rays / Mestrado / Geofisica Computacional / Mestre em Matemática Aplicada
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Homogénéisation de l'effet Hall et de la magnétorésistance dans des composites / Homogenization of the Hall effect and the magneto-resistance in compositesPater, Laurent 18 June 2013 (has links)
Les conducteurs composites sont constitués d'hétérogénéités microscopiques mais apparaissent comme homogènes à l'échelle macroscopique. La description de leur comportement nécessite l'homogénéisation des équations de conduction régissant chacune de leurs phases. Cette thèse s'intéresse à certaines lois effectives pour les conducteurs composites en présence d'un champ magnétique constant. Dans le premier chapitre, on rappelle quelques résultats d'électrophysique (effet Hall, magnétorésistance) et de la théorie de l'homogénéisation (H-convergence) ainsi que son extension à des problèmes à forte conductivité. Dans le chapitre deux, on étudie l'effet Hall dans des composites bidimensionnels à deux phases très contrastées et on compare le résultat d'homogénéisation à celui obtenu avec une structure fibrée renforcée. Le troisième chapitre généralise ce cas particulier et étend la loi comportementale obtenue à des matériaux cylindriques non périodiques sans hypothèse géométrique sur leur section. Les chapitres deux et trois soulignent des différences importantes entre la dimension deux et la dimension trois au niveau des problèmes de conduction à fort contraste. Un quatrième chapitre est consacré à l'étude de la magnétorésistance en dimension trois et met en avant une forte interaction entre la direction du champ magnétique et l'énergie dissipée dans le matériau complétant ainsi un résultat antérieur en dimension deux. / A composite conductor is composed of microscopic heterogeneities but appears as a homogeneous medium on the macroscopic scale. Describing the behavior of such materials requires the homogenization of the conduction equations which rule each of their phases. In this PhD thesis, we study a few effective laws for composite conductors in the presence of a constant magnetic field. In the first chapter, we recall a few results on electro-physics (Hall effect, magneto-resistance) and on the homogenization theory (H-convergence) as well as its extension to high-conductivity problems. In the second chapter, we study the Hall effect in two-dimensional high-contrast two-phase composites and we compare the result to the one obtained with a three-dimensional fibre-reinforced structure. The third chapter generalizes this particular case and extends the perturbation law to non-periodic cylindrical composites without any geometrical assumption on their cross section. The chapters two and three underline the gap between dimension two and dimension three in high-conductivity problems. The fourth chapter analyses the magneto-resistance in a three-dimensional composite medium and outlines a strong interaction between the direction of the magnetic field and the dissipated energy in the material; this completes a previous work on the two-dimensional case.
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Numerical Simulations of Stokes Flow by the Iterations of Boundary Conditions and Finite Difference MethodsNdou, Ndivhuwo 21 September 2018 (has links)
MSc (Applied Mathematics) / Mathematics and Applied Mathematics Department / In this study the iteration of boundary conditions method (Chizhonkov and Kargin, 2006) is
used together with the well known Finite difference numerical method to solve the Stokes
problem over a rectangular domain as well as in irregular domain. The iteration of boundary
conditions method has been applied to the Stokes problem in a rectangular domain,
2
<x<
2
,
d
2
< y <
d
2
, by the above mentioned researchers. Our main task here is
to validate the results of the approximate methods by this analytical method in case of the
rectangular domain and extend that to the case of irregular domain.The (Chizhonkov and
Kargin, 2006) algorithm is typically the best choice for validation purposes because of its
high accuracy.
It is known in literature that increasing the parameter d, which represents the ratio of the
sides, leads to slow down in convergence of the approximate methods like the conjugate
Gradients of Uzawa (Kobelkov and Olshanskii, 2000). It is therefore important that an
algorithm that converges uniformly with respect to the parameter d is considered. The
(Chizhonkov and Kargin, 2006) algorithm is typical of such an algorithm, and hence our
choice of the method in this work.
In this project the non-homogeneous Stokes problem is transformed into a homogeneous
Stokes problem and the resulting problem is then decomposed into two sub problems that
are solvable by the eigenfunction expansion method. Once all necessary coefficients of the
generalised Fourier series are known and the functions describing the boundary conditions
are prescribed and represented in terms of the Fourier series, we then proceed to formulate
the iteration of boundary conditions numerical algorithm. Finally we develop a numerical
scheme, using the finite difference methods, for solving the problem in both rectangular and
irregular domains. Coding of the numerical algorithm is done using MATLAB 9.0,R2016a
programming language, and implemented by the author. The results of the two methods in
both cases of boundary conditions are then compared for validation of our purely numerical
results. / NRF
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The flow of a compressible gas through an aggregate of mobile reacting particles /Gough, P. S. (Paul Stuart) January 1974 (has links)
No description available.
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