Iterative splitting methods for differential equations
 Responsibility
 Juergen Geiser.
 Language
 English.
 Imprint
 Boca Raton, FL : CRC Press, c2011.
 Physical description
 xxiii, 303 p. : ill. ; 24 cm.
 Series
 Chapman & Hall/CRC numerical analysis and scientific computing.
Access
Creators/Contributors
 Author/Creator
 Geiser, Juergen.
Contents/Summary
 Bibliography
 Includes bibliographical references (p. 285300) and index.
 Contents

 Introduction Model Problems Related Models for Decomposition Examples in RealLife Applications Iterative Decomposition of Ordinary Differential Equations Historical Overview Decomposition Ideas Introduction to Classical Splitting Methods Iterative Splitting Method Consistency Analysis of the Iterative Splitting Method Stability Analysis of the Iterative Splitting Method for Bounded Operators Decomposition Methods for Partial Differential Equations Iterative Schemes for Unbounded Operators Computation of the Iterative Splitting Methods: Algorithmic Part Exponential RungeKutta Methods to Compute Iterative Splitting Schemes Matrix Exponentials to Compute Iterative Splitting Schemes Algorithms Extensions of Iterative Splitting Schemes Embedded Spatial Discretization Methods Domain Decomposition Methods Based on Iterative Operator Splitting Methods Successive Approximation for TimeDependent Operators Numerical Experiments Introduction Benchmark Problems 1: Introduction Benchmark Problems 2: Comparison with Standard Splitting Methods Benchmark Problems 3: Extensions to Iterative Splitting Methods RealLife Applications Conclusion to Numerical Experiments: Discussion of Some Delicate Problems Summary and Perspectives Software Tools Software Package Unstructured Grids Software Package r3t Solving PDEs Using FIDOS Appendix Bibliography Index.
 (source: Nielsen Book Data)
 Publisher's Summary
 Iterative Splitting Methods for Differential Equations explains how to solve evolution equations via novel iterativebased splitting methods that efficiently use computational and memory resources. It focuses on systems of parabolic and hyperbolic equations, including convectiondiffusionreaction equations, heat equations, and wave equations. In the theoretical part of the book, the author discusses the main theorems and results of the stability and consistency analysis for ordinary differential equations. He then presents extensions of the iterative splitting methods to partial differential equations and spatial and timedependent differential equations. The practical part of the text applies the methods to benchmark and reallife problems, such as waste disposal, elastics wave propagation, and complex flow phenomena. The book also examines the benefits of equation decomposition. It concludes with a discussion on several useful software packages, including r3t and FIDOS. Covering a wide range of theoretical and practical issues in multiphysics and multiscale problems, this book explores the benefits of using iterative splitting schemes to solve physical problems. It illustrates how iterative operator splitting methods are excellent decomposition methods for obtaining higherorder accuracy.
(source: Nielsen Book Data)
Subjects
Bibliographic information
 Publication date
 2011
 Series
 Chapman & Hall/CRC numerical analysis and scientific computing
 Note
 "A Chapman & Hall book."
 ISBN
 9781439869826 (hbk. : acidfree paper)
 1439869820 (hbk. : acidfree paper)