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Iterative Splitting Methods for Differential Equations

Juergen Geiser
Publisher: 
Chapman & Hall/CRC
Publication Date: 
2011
Number of Pages: 
303
Format: 
Hardcover
Series: 
Chapman & Hall/CRC Numerical Analysis and Scientific Computating
Price: 
89.95
ISBN: 
9781439869826
Category: 
Monograph
We do not plan to review this book.

Introduction

 

Model Problems
Related Models for Decomposition
Examples in Real-Life 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 Runge-Kutta 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 Time-Dependent Operators

Numerical Experiments
Introduction
Benchmark Problems 1: Introduction
Benchmark Problems 2: Comparison with Standard Splitting Methods
Benchmark Problems 3: Extensions to Iterative Splitting Methods
Real-Life 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

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