Additive Operator-Difference Schemes: Splitting Schemes

Petr N. Vabishchevich

Published by De Gruyter 2014

Additive Operator-Difference Schemes

Splitting Schemes

Petr N. Vabishchevich

https://doi.org/10.1515/9783110321463

Overview
Contents

About this book

Applied mathematical modeling is concerned with solving unsteady problems. Splitting schemes are attributed to the transition from a complex problem to a chain of simpler problems. This book shows how to construct additive difference schemes (splitting schemes) to solve approximately unsteady multi-dimensional problems for PDEs. Two classes of schemes are highlighted: methods of splitting with respect to spatial variables (alternating direction methods) and schemes of splitting into physical processes. Also regionally additive schemes (domain decomposition methods) and unconditionally stable additive schemes of multi-component splitting are considered for evolutionary equations of first and second order as well as for systems of equations.

The book is written for specialists in computational mathematics and mathematical modeling. All topics are presented in a clear and accessible manner.

Author / Editor information

Petr N. Vabishchevich, Russian Academy of Sciences, Moscow, Russia.

Topics

Frontmatter Publicly Available Download PDF	i
Preface Requires Authentication Unlicensed Licensed Download PDF	v
Contents Publicly Available Download PDF	vii
Notation Requires Authentication Unlicensed Licensed Download PDF	xv
1. Introduction Requires Authentication Unlicensed Licensed Download PDF	1
2. Stability of operator-difference schemes Requires Authentication Unlicensed Licensed Download PDF	14
3. Operator splitting Requires Authentication Unlicensed Licensed Download PDF	63
4. Additive schemes of two-component splitting Requires Authentication Unlicensed Licensed Download PDF	123
5. Schemes of summarized approximation Requires Authentication Unlicensed Licensed Download PDF	144
6. Regularized additive schemes Requires Authentication Unlicensed Licensed Download PDF	167
7. Schemes based on approximations of a transition operator Requires Authentication Unlicensed Licensed Download PDF	190
8. Vector additive schemes Requires Authentication Unlicensed Licensed Download PDF	218
9. Iterative methods Requires Authentication Unlicensed Licensed Download PDF	240
10. Splitting of the operator at the time derivative Requires Authentication Unlicensed Licensed Download PDF	263
11 Equations with pairwise adjoint operators Requires Authentication Unlicensed Licensed Download PDF	291
Bibliography Requires Authentication Unlicensed Licensed Download PDF	339
Index Requires Authentication Unlicensed Licensed Download PDF	353

(Deutsch)

Language: English
Publisher: De Gruyter
Audience: Researchers in computational mathematics and mathematical modeling; academic libraries.
Pages
- Front matter: 16
- Main content: 354
Illustrations
- Illustrations: 15
- Tables: 1
Keywords: Operator Splitting; Two-Component Splitting; Summarized Approximation; Regularized Additive Schemes; Transition Operator Approximations; Vector Additive Schemes; Iterative Methods

eBook

Published: November 27, 2013
ISBN: 9783110321463

Hardcover

Published: November 15, 2013
ISBN: 9783110321432