Computer-Aided Analysis of Difference Schemes for Partial Differential Equations
VG Ganzha(Author)
Wiley (Publisher)
Published on 2. March 2011
Software
Other digital
458 pages
978-1-118-03260-2 (ISBN)
Description
Advances in computer technology have conveniently coincided with trends in numerical analysis toward increased complexity of computational algorithms based on finite difference methods. It is no longer feasible to perform stability investigation of these methods manually--and no longer necessary. As this book shows, modern computer algebra tools can be combined with methods from numerical analysis to generate programs that will do the job automatically. Comprehensive, timely, and accessible--this is the definitive reference on the application of computerized symbolic manipulations for analyzing the stability of a wide range of difference schemes. In particular, it deals with those schemes that are used to solve complex physical problems in areas such as gas dynamics, heat and mass transfer, catastrophe theory, elasticity, shallow water theory, and more.
Introducing many new applications, methods, and concepts, Computer-Aided Analysis of Difference Schemes for Partial Differential Equations * Shows how computational algebra expedites the task of stability analysis--whatever the approach to stability investigation * Covers ten different approaches for each stability method * Deals with the specific characteristics of each method and its application to problems commonly encountered by numerical modelers * Describes all basic mathematical formulas that are necessary to implement each algorithm * Provides each formula in several global algebraic symbolic languages, such as MAPLE, MATHEMATICA, and REDUCE * Includes numerous illustrations and thought-provoking examples throughout the text For mathematicians, physicists, and engineers, as well as for postgraduate students, and for anyone involved with numeric solutions for real-world physical problems, this book provides a valuable resource, a helpful guide, and a head start on developments for the twenty-first century.
Introducing many new applications, methods, and concepts, Computer-Aided Analysis of Difference Schemes for Partial Differential Equations * Shows how computational algebra expedites the task of stability analysis--whatever the approach to stability investigation * Covers ten different approaches for each stability method * Deals with the specific characteristics of each method and its application to problems commonly encountered by numerical modelers * Describes all basic mathematical formulas that are necessary to implement each algorithm * Provides each formula in several global algebraic symbolic languages, such as MAPLE, MATHEMATICA, and REDUCE * Includes numerous illustrations and thought-provoking examples throughout the text For mathematicians, physicists, and engineers, as well as for postgraduate students, and for anyone involved with numeric solutions for real-world physical problems, this book provides a valuable resource, a helpful guide, and a head start on developments for the twenty-first century.
More details
Language
English
Place of publication
New York
United States
Target group
Professional and scholarly
Dimensions
Height: 239 mm
Width: 167 mm
Thickness: 36 mm
Weight
816 gr
ISBN-13
978-1-118-03260-2 (9781118032602)
Copyright in bibliographic data is held by Nielsen Book Services Limited or its licensors: all rights reserved.
Schweitzer Classification
Other editions
Additional editions

Victor G. Ganzha | E. V. Vorozhtsov
Computer-Aided Analysis of Difference Schemes for Partial Differential Equations
E-Book
03/2011
Wiley
€207.99
Available for download
Person
VICTOR G. GANZHA is Visiting Professor of Mathematics with the Faculty of Mathematics and Informatics at the University of Kassel, Germany, where he presents lecture courses on advanced computer algebra systems and their applications to higher mathematics and numerical analysis. He is coauthor of Differentialgleichungen mit Mathematica. E. V. VOROZHTSOV is a research scientist at the Russian Academy of Sciences in Novosibirsk, Russia, and Professor of Mathematics with the Faculty of Flying Vehicles at the Novosibirsk State Technical University. He is coauthor of Methods for the Localization of Singularities in Numerical Solutions of Gas Dynamics Problems.
Content
The Necessary Basics from the Stability Theory of Difference Schemes and Polynomials. Symbolic-Numerical Method for the Stability Investigation of Difference Schemes on a Computer. Application of Optimization Methods to the Stability Analysis of Difference Schemes. Stability Analysis of Difference Schemes by Catastrophe Theory Methods. Construction of Multiply Connected Stability Regions of Difference Schemes by Computer Algebra and Pattern Recognition. Maximally Stable Difference Schemes. Stability Analysis of Nonlinear Difference Schemes. Symbolic Computation of Differential Approximations. Appendices. Index.