Time-Dependent Problems and Difference Methods - Hardcover

Gustafsson, Bertil; Kreiss, Heinz-Otto; Oliger, Joseph

Hardcover

ISBN 10: 0470900563 ISBN 13: 9780470900567

Publisher: Wiley, 2013

Synopsis

Praise for the First Edition

". . . fills a considerable gap in the numerical analysis literature by providing a self-contained treatment . . . this is an important work written in a clear style . . . warmly recommended to any graduate student or researcher in the field of the numerical solution of partial differential equations."
―SIAM Review

Time-Dependent Problems and Difference Methods, Second Edition continues to provide guidance for the analysis of difference methods for computing approximate solutions to partial differential equations for time-dependent problems. The book treats differential equations and difference methods with a parallel development, thus achieving a more useful analysis of numerical methods.

The Second Edition presents hyperbolic equations in great detail as well as new coverage on second-order systems of wave equations including acoustic waves, elastic waves, and Einstein equations. Compared to first-order hyperbolic systems, initial-boundary value problems for such systems contain new properties that must be taken into account when analyzing stability. Featuring the latest material in partial differential equations with new theorems, examples, and illustrations,Time-Dependent Problems and Difference Methods, Second Edition also includes:

• High order methods on staggered grids
• Extended treatment of Summation By Parts operators and their application to second-order derivatives
• Simplified presentation of certain parts and proofs

Time-Dependent Problems and Difference Methods, Second Edition is an ideal reference for physical scientists, engineers, numerical analysts, and mathematical modelers who use numerical experiments to test designs and to predict and investigate physical phenomena. The book is also excellent for graduate-level courses in applied mathematics and scientific computations.

About this title

From the Publisher

Describes the construction and analysis of numerical methods for partial differential equations, particularly for time dependent problems arising from scientific and engineering industries. A substantial portion of the text concentrates on initial boundary value problems and their numerical techniques, stressing error bounds and estimates as well as the sufficient results needed to justify the methods used with the applications. The problems are practical and derived from nonlinear calculations. The development of the hyperbolic equations is more complete and detailed than other parabolic equations or equations of any type. Includes a discussion of the design and analysis of finite difference and Fourier methods.

From the Inside Flap

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 analysts, mathematical modelers, and graduate students of applied mathematics and scientific computations.

About this edition

• Publisher: Wiley
• Publication date: 2013
• ISBN 10: 0470900563
• ISBN 13: 9780470900567
• Binding: Hardcover
• Edition number: 2
• Number of pages: 528