Iterative Splitting Methods for Differential Equations: 1st Edition (Paperback) book cover

Iterative Splitting Methods for Differential Equations

1st Edition

By Juergen Geiser

Chapman and Hall/CRC

320 pages | 71 B/W Illus.

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Description

Iterative Splitting Methods for Differential Equations explains how to solve evolution equations via novel iterative-based splitting methods that efficiently use computational and memory resources. It focuses on systems of parabolic and hyperbolic equations, including convection-diffusion-reaction 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 time-dependent differential equations.

The practical part of the text applies the methods to benchmark and real-life 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 higher-order accuracy.

Table of Contents

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

About the Author

Juergen Geiser is a researcher in the Department of Mathematics at the Humboldt-University of Berlin. His research interests include numerical and computational analysis, partial differential equations, decomposition and discretization methods for hyperbolic and parabolic equations, optimization, scientific computing, and interface analysis.

About the Series

Chapman & Hall/CRC Numerical Analysis and Scientific Computing Series

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Subject Categories

BISAC Subject Codes/Headings:
MAT000000
MATHEMATICS / General
MAT003000
MATHEMATICS / Applied
MAT021000
MATHEMATICS / Number Systems