Decomposition methods for differential equations theory and applications 1st Edition by Juergen Geiser ISBN 1138114146 978-1138114142

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ISBN 10:  1138114146 

ISBN 13: 978-1138114142

Author:   Juergen Geiser

Decomposition Methods for Differential Equations: Theory and Applications describes the analysis of numerical methods for evolution equations based on temporal and spatial decomposition methods. It covers real-life problems, the underlying decomposition and discretization, the stability and consistency analysis of the decomposition methods, and numerical results.

The book focuses on the modeling of selected multi-physics problems, before introducing decomposition analysis. It presents time and space discretization, temporal decomposition, and the combination of time and spatial decomposition methods for parabolic and hyperbolic equations. The author then applies these methods to numerical problems, including test examples and real-world problems in physical and engineering applications. For the computational results, he uses various software tools, such as MATLAB®, R3T, WIAS-HiTNIHS, and OPERA-SPLITT.

Exploring iterative operator-splitting methods, this book shows how to use higher-order discretization methods to solve differential equations. It discusses decomposition methods and their effectiveness, combination possibility with discretization methods, multi-scaling possibilities, and stability to initial and boundary values problems.

Table of contents: 

1 Preface
2 Introduction
3 Modeling: Multi-Physics Problems
4 Introduction
5 Models for Multi-Physics Problems
6 Examples for Multi-Physics Problems
7 Abstract Decomposition and Discretization Methods
8 Decomposition
9 Discretization
10 Time-Decomposition Methods for Parabolic Equations
11 Introduction for the Splitting Methods
12 Iterative Operator-Splitting Methods for Bounded Operators
13 Iterative Operator-Splitting Methods for Unbounded Operators
14 Decomposition Methods for Hyperbolic Equations
15 Introduction for the Splitting Methods
16 ADI Methods and LOD Methods
17 Iterative Operator-Splitting Methods for Wave Equations
18 Parallelization of Time Decomposition Methods
19 Nonlinear Iterative Operator-Splitting Methods
20 Spatial Decomposition Methods
21 Domain Decomposition Methods Based on Iterative Operator-Splitting Methods
22 Schwarz Waveform-Relaxation Methods
23 Overlapping Schwarz Waveform Relaxation for the Solution of Convection-Diffusion-Reaction Equation
24 Numerical Experiments
25 Introduction
26 Benchmark Problems for the Time Decomposition Methods for Ordinary Differential and Parabolic Equations
27 Benchmark Problems for Spatial Decomposition Methods: Schwarz Waveform-Relaxation Method
28 Benchmark Problems: Hyperbolic Equations
29 Real-Life Applications

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Tags: Juergen Geiser, Decomposition methods, differential equations, theory and applications