Additive Operator-Difference Schemes : : Splitting Schemes / / Petr N. Vabishchevich.

• Superior document: Title is part of eBook package: De Gruyter DGBA Backlist Complete English Language 2000-2014 PART1
• VerfasserIn: Vabishchevich, Petr N.,
• Place / Publishing House: Berlin ;, Boston : : De Gruyter, , [2013]; ©2014
• Year of Publication: 2013
• Language: English
• Physical Description: 1 online resource (354 p.)

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.

Table of Contents

Frontmatter -- Preface -- Contents -- Notation -- 1. Introduction -- 2. Stability of operator-difference schemes -- 3. Operator splitting -- 4. Additive schemes of two-component splitting -- 5. Schemes of summarized approximation -- 6. Regularized additive schemes -- 7. Schemes based on approximations of a transition operator -- 8. Vector additive schemes -- 9. Iterative methods -- 10. Splitting of the operator at the time derivative -- 11 Equations with pairwise adjoint operators -- Bibliography -- Index