Difference schemes with operator factors. (English) Zbl 1018.65103

Samarskii, A. A.; Matus, P. P.; Vabishchevich, P. N.

Mathematics and its Applications (Dordrecht). 546. Dordrecht: Kluwer Academic Publishers. x, 384 p. (2002).

This book reflects the modern level of the theory of problem solving differential methods in mathematical physics. The main results concern the stability and convergence of finite difference and/or finite element solutions of systems of partial differential equation’s. The book contains the numerical analysis of two and three level difference schemes, difference schemes for nonstationary equations, schemes on adaptive grids and difference schemes of domain decomposition for non-stationary problems. The book is intended for specialist in numerical methods of solution of mathematical physics problems; the exposition is easily understood by senior students of universities.

Reviewer: Vit Dolejsi (Praha)

MSC:

65M06	Finite difference methods for initial value and initial-boundary value problems involving PDEs
65-02	Research exposition (monographs, survey articles) pertaining to numerical analysis
35Qxx	Partial differential equations of mathematical physics and other areas of application
65M12	Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
65M50	Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs
65M55	Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs
00A71	General theory of mathematical modeling

Keywords:

partial differential equations; finite difference method; operator factors; textbook; stability; convergence; finite element; domain decomposition