Nonlinear stability of finite volume methods for hyperbolic conservation laws and well-balanced schemes for sources. (English) Zbl 1086.65091

Bouchut, François

Frontiers in Mathematics. Basel: Birkhäuser (ISBN 3-7643-6665-6/pbk). viii, 135 p. (2004).

This is a very interesting and useful book which provides a systematic presentation of the theory of finite volume methods and numerical simulations for hyperbolic systems of conservation laws.
It contains six chapters as follows: Quasilinear systems and conservation laws (introductory chapter); Conservative schemes; Source terms; Nonconservative schemes; Multidimensional finite volumes with sources; Numerical tests with source.
The author provides a unified approach and notation to the study of nonlinear stability of finite volume methods for hyperbolic systems of conservation laws as the accent is put on the development of tools and design of schemes. The exposition of the book is very clear. It will be a very useful tool for the researchers in this field as well as for engineers.

Reviewer: Emil Minchev (Russe)

MSC:

65M12	Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
65-02	Research exposition (monographs, survey articles) pertaining to numerical analysis
35L05	Wave equation
65M06	Finite difference methods for initial value and initial-boundary value problems involving PDEs

Keywords:

finite volume methods; hyperbolic conservation laws; nonlinear stability; textbook; numerical examples

Software:

HLLE; HE-E1GODF