Partial Differential Equations With Numerical Methods

Partial Differential Equations with Numerical Methods PDF
Author: Stig Larsson
Publisher: Springer Science & Business Media
ISBN: 3540887067
Size: 58.60 MB
Format: PDF, Docs
Category : Mathematics
Languages : en
Pages : 262
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Partial Differential Equations With Numerical Methods

by Stig Larsson, Partial Differential Equations With Numerical Methods Books available in PDF, EPUB, Mobi Format. Download Partial Differential Equations With Numerical Methods books, The main theme is the integration of the theory of linear PDE and the theory of finite difference and finite element methods. For each type of PDE, elliptic, parabolic, and hyperbolic, the text contains one chapter on the mathematical theory of the differential equation, followed by one chapter on finite difference methods and one on finite element methods. The chapters on elliptic equations are preceded by a chapter on the two-point boundary value problem for ordinary differential equations. Similarly, the chapters on time-dependent problems are preceded by a chapter on the initial-value problem for ordinary differential equations. There is also one chapter on the elliptic eigenvalue problem and eigenfunction expansion. The presentation does not presume a deep knowledge of mathematical and functional analysis. The required background on linear functional analysis and Sobolev spaces is reviewed in an appendix. The book is suitable for advanced undergraduate and beginning graduate students of applied mathematics and engineering.


Numerical Methods For Partial Differential Equations

Numerical Methods for Partial Differential Equations PDF
Author: William F. Ames
Publisher: Academic Press
ISBN: 0080571301
Size: 40.24 MB
Format: PDF, Kindle
Category : Mathematics
Languages : en
Pages : 451
View: 2583

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Numerical Methods For Partial Differential Equations

by William F. Ames, Numerical Methods For Partial Differential Equations Books available in PDF, EPUB, Mobi Format. Download Numerical Methods For Partial Differential Equations books, This volume is designed as an introduction to the concepts of modern numerical analysis as they apply to partial differential equations. The book contains many practical problems and their solutions, but at the same time, strives to expose the pitfalls--such as overstability, consistency requirements, and the danger of extrapolation to nonlinear problems methods used on linear problems. Numerical Methods for Partial Differential Equations, Third Edition reflects the great accomplishments that have taken place in scientific computation in the fifteen years since the Second Edition was published. This new edition is a drastic revision of the previous one, with new material on boundary elements, spectral methods, the methods of lines, and invariant methods. At the same time, the new edition retains the self-contained nature of the older version, and shares the clarity of its exposition and the integrity of its presentation. Material on finite elements and finite differences have been merged, and now constitute equal partners Additional material has been added on boundary elements, spectral methods, the method of lines, and invariant methods References have been updated, and reflect the additional material Self-contained nature of the Second Edition has been maintained Very suitable for PDE courses


Numerical Solution Of Partial Differential Equations

Numerical Solution of Partial Differential Equations PDF
Author: Gordon D. Smith
Publisher: Oxford University Press
ISBN: 9780198596509
Size: 30.86 MB
Format: PDF, ePub
Category : Mathematics
Languages : en
Pages : 337
View: 923

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Numerical Solution Of Partial Differential Equations

by Gordon D. Smith, Numerical Solution Of Partial Differential Equations Books available in PDF, EPUB, Mobi Format. Download Numerical Solution Of Partial Differential Equations books, Substantially revised, this authoritative study covers the standard finite difference methods of parabolic, hyperbolic, and elliptic equations, and includes the concomitant theoretical work on consistency, stability, and convergence. The new edition includes revised and greatly expanded sections on stability based on the Lax-Richtmeyer definition, the application of Pade approximants to systems of ordinary differential equations for parabolic and hyperbolic equations, and a considerably improved presentation of iterative methods. A fast-paced introduction to numerical methods, this will be a useful volume for students of mathematics and engineering, and for postgraduates and professionals who need a clear, concise grounding in this discipline.


Partial Differential Equations

Partial Differential Equations PDF
Author: J. Necas
Publisher: CRC Press
ISBN: 9781584880226
Size: 31.11 MB
Format: PDF, ePub, Docs
Category : Mathematics
Languages : en
Pages : 360
View: 6315

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Partial Differential Equations

by J. Necas, Partial Differential Equations Books available in PDF, EPUB, Mobi Format. Download Partial Differential Equations books, As a satellite conference of the 1998 International Mathematical Congress and part of the celebration of the 650th anniversary of Charles University, the Partial Differential Equations Theory and Numerical Solution conference was held in Prague in August, 1998. With its rich scientific program, the conference provided an opportunity for almost 200 participants to gather and discuss emerging directions and recent developments in partial differential equations (PDEs). This volume comprises the Proceedings of that conference. In it, leading specialists in partial differential equations, calculus of variations, and numerical analysis present up-to-date results, applications, and advances in numerical methods in their fields. Conference organizers chose the contributors to bring together the scientists best able to present a complex view of problems, starting from the modeling, passing through the mathematical treatment, and ending with numerical realization. The applications discussed include fluid dynamics, semiconductor technology, image analysis, motion analysis, and optimal control. The importance and quantity of research carried out around the world in this field makes it imperative for researchers, applied mathematicians, physicists and engineers to keep up with the latest developments. With its panel of international contributors and survey of the recent ramifications of theory, applications, and numerical methods, Partial Differential Equations: Theory and Numerical Solution provides a convenient means to that end.


Mathematical And Numerical Methods For Partial Differential Equations

Mathematical and Numerical Methods for Partial Differential Equations PDF
Author: Joël Chaskalovic
Publisher: Springer
ISBN: 3319035630
Size: 32.69 MB
Format: PDF, Mobi
Category : Mathematics
Languages : en
Pages : 358
View: 4256

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Mathematical And Numerical Methods For Partial Differential Equations

by Joël Chaskalovic, Mathematical And Numerical Methods For Partial Differential Equations Books available in PDF, EPUB, Mobi Format. Download Mathematical And Numerical Methods For Partial Differential Equations books, This self-tutorial offers a concise yet thorough introduction into the mathematical analysis of approximation methods for partial differential equation. A particular emphasis is put on finite element methods. The unique approach first summarizes and outlines the finite-element mathematics in general and then in the second and major part, formulates problem examples that clearly demonstrate the techniques of functional analysis via numerous and diverse exercises. The solutions of the problems are given directly afterwards. Using this approach, the author motivates and encourages the reader to actively acquire the knowledge of finite- element methods instead of passively absorbing the material as in most standard textbooks. This English edition is based on the Finite Element Methods for Engineering Sciences by Joel Chaskalovic.


Asymptotic And Numerical Methods For Partial Differential Equations With Critical Parameters

Asymptotic and Numerical Methods for Partial Differential Equations with Critical Parameters PDF
Author: H.G. Kaper
Publisher: Springer Science & Business Media
ISBN: 9401118108
Size: 41.74 MB
Format: PDF, ePub, Docs
Category : Mathematics
Languages : en
Pages : 372
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Asymptotic And Numerical Methods For Partial Differential Equations With Critical Parameters

by H.G. Kaper, Asymptotic And Numerical Methods For Partial Differential Equations With Critical Parameters Books available in PDF, EPUB, Mobi Format. Download Asymptotic And Numerical Methods For Partial Differential Equations With Critical Parameters books, This volume contains the proceedings of the NATO Advanced Research Workshop on "Asymptotic-induced Numerical Methods for Partial Differ ential Equations, Critical Parameters, and Domain Decomposition," held at Beaune (France), May 25-28, 1992. The purpose of the workshop was to stimulate the integration of asymp totic analysis, domain decomposition methods, and symbolic manipulation tools for the numerical solution of partial differential equations (PDEs) with critical parameters. A workshop on the same topic was held at Argonne Na tional Laboratory in February 1990. (The proceedings were published under the title Asymptotic Analysis and the Numerical Solu.tion of Partial Differ ential Equations, Hans G. Kaper and Marc Garbey, eds., Lecture Notes in Pure and Applied Mathematics. Vol. 130, ·Marcel Dekker, Inc., New York, 1991.) In a sense, the present proceedings represent a progress report on the topic area. Comparing the two sets of proceedings, we see an increase in the quantity as well as the quality of the contributions. 110re research is being done in the topic area, and the interest covers serious, nontrivial problems. We are pleased with this outcome and expect to see even more advances in the next few years as the field progresses.


Partial Differential Equations With Numerical Methods

Partial Differential Equations with Numerical Methods PDF
Author: Stig Larsson
Publisher: Springer Science & Business Media
ISBN: 9783540017721
Size: 57.11 MB
Format: PDF
Category : Mathematics
Languages : en
Pages : 259
View: 1985

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Partial Differential Equations With Numerical Methods

by Stig Larsson, Partial Differential Equations With Numerical Methods Books available in PDF, EPUB, Mobi Format. Download Partial Differential Equations With Numerical Methods books, This softcover reprint of a very popular book presents a very well written and systematic introduction to the finite difference and finite element methods for the numerical solution of the basic types of linear partial differential equations (PDE).


Numerical Methods For Stochastic Partial Differential Equations With White Noise

Numerical Methods for Stochastic Partial Differential Equations with White Noise PDF
Author: Zhongqiang Zhang
Publisher: Springer
ISBN: 3319575112
Size: 15.28 MB
Format: PDF, ePub, Mobi
Category : Mathematics
Languages : en
Pages : 394
View: 703

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Numerical Methods For Stochastic Partial Differential Equations With White Noise

by Zhongqiang Zhang, Numerical Methods For Stochastic Partial Differential Equations With White Noise Books available in PDF, EPUB, Mobi Format. Download Numerical Methods For Stochastic Partial Differential Equations With White Noise books, This book covers numerical methods for stochastic partial differential equations with white noise using the framework of Wong-Zakai approximation. The book begins with some motivational and background material in the introductory chapters and is divided into three parts. Part I covers numerical stochastic ordinary differential equations. Here the authors start with numerical methods for SDEs with delay using the Wong-Zakai approximation and finite difference in time. Part II covers temporal white noise. Here the authors consider SPDEs as PDEs driven by white noise, where discretization of white noise (Brownian motion) leads to PDEs with smooth noise, which can then be treated by numerical methods for PDEs. In this part, recursive algorithms based on Wiener chaos expansion and stochastic collocation methods are presented for linear stochastic advection-diffusion-reaction equations. In addition, stochastic Euler equations are exploited as an application of stochastic collocation methods, where a numerical comparison with other integration methods in random space is made. Part III covers spatial white noise. Here the authors discuss numerical methods for nonlinear elliptic equations as well as other equations with additive noise. Numerical methods for SPDEs with multiplicative noise are also discussed using the Wiener chaos expansion method. In addition, some SPDEs driven by non-Gaussian white noise are discussed and some model reduction methods (based on Wick-Malliavin calculus) are presented for generalized polynomial chaos expansion methods. Powerful techniques are provided for solving stochastic partial differential equations. This book can be considered as self-contained. Necessary background knowledge is presented in the appendices. Basic knowledge of probability theory and stochastic calculus is presented in Appendix A. In Appendix B some semi-analytical methods for SPDEs are presented. In Appendix C an introduction to Gauss quadrature is provided. In Appendix D, all the conclusions which are needed for proofs are presented, and in Appendix E a method to compute the convergence rate empirically is included. In addition, the authors provide a thorough review of the topics, both theoretical and computational exercises in the book with practical discussion of the effectiveness of the methods. Supporting Matlab files are made available to help illustrate some of the concepts further. Bibliographic notes are included at the end of each chapter. This book serves as a reference for graduate students and researchers in the mathematical sciences who would like to understand state-of-the-art numerical methods for stochastic partial differential equations with white noise.


The Numerical Solution Of Ordinary And Partial Differential Equations

The Numerical Solution of Ordinary and Partial Differential Equations PDF
Author: Granville Sewell
Publisher: John Wiley & Sons
ISBN: 0471742007
Size: 28.17 MB
Format: PDF, ePub, Docs
Category : Mathematics
Languages : en
Pages : 352
View: 1832

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The Numerical Solution Of Ordinary And Partial Differential Equations

by Granville Sewell, The Numerical Solution Of Ordinary And Partial Differential Equations Books available in PDF, EPUB, Mobi Format. Download The Numerical Solution Of Ordinary And Partial Differential Equations books,


Partial Differential Equations

Partial Differential Equations PDF
Author: Mark S. Gockenbach
Publisher: SIAM
ISBN: 0898719356
Size: 28.55 MB
Format: PDF, ePub
Category : Mathematics
Languages : en
Pages : 654
View: 7542

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Partial Differential Equations

by Mark S. Gockenbach, Partial Differential Equations Books available in PDF, EPUB, Mobi Format. Download Partial Differential Equations books, A fresh, forward-looking undergraduate textbook that treats the finite element method and classical Fourier series method with equal emphasis.