Asymptotic and Numerical Methods for Partial Differential Equations with Critical Parameters

Asymptotic and Numerical Methods for Partial Differential Equations with Critical Parameters
Title Asymptotic and Numerical Methods for Partial Differential Equations with Critical Parameters PDF eBook
Author H.G. Kaper
Publisher Springer Science & Business Media
Pages 371
Release 2012-12-06
Genre Mathematics
ISBN 9401118108

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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

Partial Differential Equations
Title Partial Differential Equations PDF eBook
Author Walter A. Strauss
Publisher John Wiley & Sons
Pages 467
Release 2007-12-21
Genre Mathematics
ISBN 0470054565

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Our understanding of the fundamental processes of the natural world is based to a large extent on partial differential equations (PDEs). The second edition of Partial Differential Equations provides an introduction to the basic properties of PDEs and the ideas and techniques that have proven useful in analyzing them. It provides the student a broad perspective on the subject, illustrates the incredibly rich variety of phenomena encompassed by it, and imparts a working knowledge of the most important techniques of analysis of the solutions of the equations. In this book mathematical jargon is minimized. Our focus is on the three most classical PDEs: the wave, heat and Laplace equations. Advanced concepts are introduced frequently but with the least possible technicalities. The book is flexibly designed for juniors, seniors or beginning graduate students in science, engineering or mathematics.

Asymptotic Analysis and the Numerical Solution of Partial Differential Equations

Asymptotic Analysis and the Numerical Solution of Partial Differential Equations
Title Asymptotic Analysis and the Numerical Solution of Partial Differential Equations PDF eBook
Author Hans G. Kaper
Publisher CRC Press
Pages 290
Release 1991-02-25
Genre Mathematics
ISBN 9780585319674

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Integrates two fields generally held to be incompatible, if not downright antithetical, in 16 lectures from a February 1990 workshop at the Argonne National Laboratory, Illinois. The topics, of interest to industrial and applied mathematicians, analysts, and computer scientists, include singular per

Domain Decomposition Methods for the Numerical Solution of Partial Differential Equations

Domain Decomposition Methods for the Numerical Solution of Partial Differential Equations
Title Domain Decomposition Methods for the Numerical Solution of Partial Differential Equations PDF eBook
Author Tarek Mathew
Publisher Springer Science & Business Media
Pages 775
Release 2008-06-25
Genre Mathematics
ISBN 354077209X

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Domain decomposition methods are divide and conquer computational methods for the parallel solution of partial differential equations of elliptic or parabolic type. The methodology includes iterative algorithms, and techniques for non-matching grid discretizations and heterogeneous approximations. This book serves as a matrix oriented introduction to domain decomposition methodology. A wide range of topics are discussed include hybrid formulations, Schwarz, and many more.

Acta Numerica 1994: Volume 3

Acta Numerica 1994: Volume 3
Title Acta Numerica 1994: Volume 3 PDF eBook
Author Arieh Iserles
Publisher Cambridge University Press
Pages 582
Release 1994-07-29
Genre Mathematics
ISBN 9780521461818

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Acta Numerica is an annual volume presenting survey papers in numerical analysis accessible to graduate students and researchers. Highlights of the 1994 issue are articles on domain decomposition, mesh adaption, pseudospectral methods and neural networks.

Partial Differential Equations V

Partial Differential Equations V
Title Partial Differential Equations V PDF eBook
Author M.V. Fedoryuk
Publisher Springer Science & Business Media
Pages 248
Release 2012-12-06
Genre Mathematics
ISBN 3642584233

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In this paper we shall discuss the construction of formal short-wave asymp totic solutions of problems of mathematical physics. The topic is very broad. It can somewhat conveniently be divided into three parts: 1. Finding the short-wave asymptotics of a rather narrow class of problems, which admit a solution in an explicit form, via formulas that represent this solution. 2. Finding formal asymptotic solutions of equations that describe wave processes by basing them on some ansatz or other. We explain what 2 means. Giving an ansatz is knowing how to give a formula for the desired asymptotic solution in the form of a series or some expression containing a series, where the analytic nature of the terms of these series is indicated up to functions and coefficients that are undetermined at the first stage of consideration. The second stage is to determine these functions and coefficients using a direct substitution of the ansatz in the equation, the boundary conditions and the initial conditions. Sometimes it is necessary to use different ansiitze in different domains, and in the overlapping parts of these domains the formal asymptotic solutions must be asymptotically equivalent (the method of matched asymptotic expansions). The basis for success in the search for formal asymptotic solutions is a suitable choice of ansiitze. The study of the asymptotics of explicit solutions of special model problems allows us to "surmise" what the correct ansiitze are for the general solution.

SIAM Journal on Scientific Computing

SIAM Journal on Scientific Computing
Title SIAM Journal on Scientific Computing PDF eBook
Author
Publisher
Pages 800
Release 2004
Genre Electronic journals
ISBN

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