Iterative Splitting Methods for Differential Equations 1st Edition by Juergen Geiser ISBN 978-1138111905 1138111902

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Product details: 

ISBN 10:  1138111902

ISBN 13: 978-1138111905

Author:  Juergen Geiser

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: 

1. Model Problems

2. Related Models for Decomposition

3. Examples in Real-Life Applications

4. Iterative Decomposition of Ordinary Differential Equations

5. Historical Overview

6. Decomposition Ideas

7. Introduction to Classical Splitting Methods

8. Iterative Splitting Method

9. Consistency Analysis of the Iterative Splitting Method

10. Stability Analysis of the Iterative Splitting Method for Bounded Operators

11. Decomposition Methods for Partial Differential Equations

12. Iterative Schemes for Unbounded Operators

13. Computation of the Iterative Splitting Methods: Algorithmic Part

14. Exponential Runge-Kutta Methods to Compute Iterative Splitting Schemes

15. Matrix Exponentials to Compute Iterative Splitting Schemes

16. Algorithms

17. Extensions of Iterative Splitting Schemes

18. Embedded Spatial Discretization Methods

19. Domain Decomposition Methods Based on Iterative Operator Splitting Methods

20. Successive Approximation for Time-Dependent Operators

21. Numerical Experiments

22. Introduction

23. Benchmark Problems 1: Introduction

24. Benchmark Problems 2: Comparison with Standard Splitting Methods

25. Benchmark Problems 3: Extensions to Iterative Splitting Methods

26. Real-Life Applications

27. Conclusion to Numerical Experiments: Discussion of Some Delicate Problems

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Tags: Juergen Geiser, Iterative Splitting Methods, Differential Equations