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Pure and Applied Mathematics: a Wiley Series of Texts, Monographs and Tracts Ser.: Time Dependent Problems and Difference Methods by Bertil Gustafsson, Heinz-Otto Kreiss and Joseph Oliger (1996, Hardcover)

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About this product

Product Identifiers

PublisherWiley & Sons, Incorporated, John

ISBN-100471507342

ISBN-139780471507345

eBay Product ID (ePID)580512

Product Key Features

Number of Pages656 Pages

LanguageEnglish

Publication NameTime Dependent Problems and Difference Methods

SubjectNumber Systems, Differential Equations / Partial

Publication Year1996

TypeTextbook

AuthorBertil Gustafsson, Heinz-Otto Kreiss, Joseph Oliger

Subject AreaMathematics

SeriesPure and Applied Mathematics: a Wiley Series of Texts, Monographs and Tracts Ser.

FormatHardcover

Dimensions

Item Height1.9 in

Item Weight0 Oz

Item Length9.3 in

Item Width6.3 in

Additional Product Features

Edition Number1

Intended AudienceScholarly & Professional

LCCN94-044176

Dewey Edition20

Series Volume Number24

IllustratedYes

Dewey Decimal51/.353

Table Of ContentPROBLEMS WITH PERIODIC SOLUTIONS. Fourier Series and Trigonometric Interpolation. Model Equations. Higher Order Accuracy. Well-Posed Problems. Stability and Convergence for Numerical Approximations of Linear and Nonlinear Problems. Hyperbolic Equations and Numerical Methods. Parabolic Equations and Numerical Methods. Problems with Discontinuous Solutions. INITIAL-BOUNDARY-VALUE PROBLEMS. Initial-Boundary-Value Problems. The Laplace Transform Method for Initial-Boundary-Value Problems. The Energy Method for Difference Approximations. The Laplace Transform Method for Difference Approximations. The Laplace Transform Method for Fully Discrete Approximations: Normal Mode Analysis. Appendices. References. Index.

SynopsisTime dependent problems frequently pose challenges in areas of science and engineering dealing with numerical analysis, scientific computation, mathematical models, and most importantly-numerical experiments intended to analyze physical behavior and test design. Time Dependent Problems and Difference Methods addresses these various industrial considerations in a pragmatic and detailed manner, giving special attention to time dependent problems in its coverage of the derivation and analysis of numerical methods for computational approximations to Partial Differential Equations (PDEs). The book is written in two parts. Part I discusses problems with periodic solutions; Part II proceeds to discuss initial boundary value problems for partial differential equations and numerical methods for them. The problems with periodic solutions have been chosen because they allow the application of Fourier analysis without the complication that arises from the infinite domain for the corresponding Cauchy problem. Furthermore, the analysis of periodic problems provides necessary conditions when constructing methods for initial boundary value problems. Much of the material included in Part II appears for the first time in this book. The authors draw on their own interests and combined extensive experience in applied mathematics and computer science to bring about this practical and useful guide. They provide complete discussions of the pertinent theorems and back them up with examples and illustrations. For physical scientists, engineers, or anyone who uses numerical experiments to test designs or to predict and investigate physical phenomena, this invaluable guide is destined to become a constant companion. Time Dependent Problems and Difference Methods is also extremely useful to numerical analysts, mathematical modelers, and graduate students of applied mathematics and scientific computations. What Every Physical Scientist and Engineer Needs to Know About Time Dependent Problems . . . Time Dependent Problems and Difference Methods covers the analysis of numerical methods for computing approximate solutions to partial differential equations for time dependent problems. This original book includes for the first time a concrete discussion of initial boundary value problems for partial differential equations. The authors have redone many of these results especially for this volume, including theorems, examples, and over one hundred illustrations. The book takes some less-than-obvious approaches to developing its material: Treats differential equations and numerical methods with a parallel development, thus achieving a more useful analysis of numerical methods Covers hyperbolic equations in particularly great detail Emphasizes error bounds and estimates, as well as the sufficient results needed to justify the methods used for applications Time Dependent Problems and Difference Methods is written for physical scientists and engineers who use numerical experiments to test designs or to predict and investigate physical phenomena. It is also extremely useful to numerical analysts, mathematical modelers, and graduate students of applied mathematics and scientific computations., Time dependent problems frequently pose challenges in areas of science and engineering dealing with numerical analysis, scientific computation, mathematical models, and most importantly--numerical experiments intended to analyze physical behavior and test design., Time dependent problems frequently pose challenges in areas of science and engineering dealing with numerical analysis, scientific computation, mathematical models, and most importantly--numerical experiments intended to analyze physical behavior and test design. Time Dependent Problems and Difference Methods addresses these various industrial considerations in a pragmatic and detailed manner, giving special attention to time dependent problems in its coverage of the derivation and analysis of numerical methods for computational approximations to Partial Differential Equations (PDEs). The book is written in two parts. Part I discusses problems with periodic solutions; Part II proceeds to discuss initial boundary value problems for partial differential equations and numerical methods for them. The problems with periodic solutions have been chosen because they allow the application of Fourier analysis without the complication that arises from the infinite domain for the corresponding Cauchy problem. Furthermore, the analysis of periodic problems provides necessary conditions when constructing methods for initial boundary value problems. Much of the material included in Part II appears for the first time in this book. The authors draw on their own interests and combined extensive experience in applied mathematics and computer science to bring about this practical and useful guide. They provide complete discussions of the pertinent theorems and back them up with examples and illustrations. For physical scientists, engineers, or anyone who uses numerical experiments to test designs or to predict and investigate physical phenomena, this invaluable guide is destined to become a constant companion. Time Dependent Problems and Difference Methods is also extremely useful to numerical analysts, mathematical modelers, and graduate students of applied mathematics and scientific computations. What Every Physical Scientist and Engineer Needs to Know About Time Dependent Problems . . . Time Dependent Problems and Difference Methods covers the analysis of numerical methods for computing approximate solutions to partial differential equations for time dependent problems. This original book includes for the first time a concrete discussion of initial boundary value problems for partial differential equations. The authors have redone many of these results especially for this volume, including theorems, examples, and over one hundred illustrations. The book takes some less-than-obvious approaches to developing its material: * Treats differential equations and numerical methods with a parallel development, thus achieving a more useful analysis of numerical methods * Covers hyperbolic equations in particularly great detail * Emphasizes error bounds and estimates, as well as the sufficient results needed to justify the methods used for applications Time Dependent Problems and Difference Methods is written for physical scientists and engineers who use numerical experiments to test designs or to predict and investigate physical phenomena. It is also extremely useful to numerical analysts, mathematical modelers, and graduate students of applied mathematics and scientific computations.

LC Classification NumberQA374.G974 1995