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Finite volume methods for hyperbolic problems. (English) Zbl 1010.65040
Cambridge Texts in Applied Mathematics. Cambridge: Cambridge University Press. xix, 558 p. (2002).
The book gives an introduction to hyperbolic partial differential equations and numerical methods for their approximate solution. It covers aspects of mathematical theory as well as numerical practice involving a variety of (linear and nonlinear) applications. The text is very well written and can serve for self-study as well as an accompanying text book for teaching purposes.
A lot of examples and exercises supports this, in particular, since all numerical methods presented are implemented in a software package available on the web. An extensive bibliography with nearly 500 entries provides all-embracing suggestions for further reading. In summary, the book can be regarded as a very sound and comprehensive introduction into hyperbolic problems and their numerical treatment, which can be very helpful for students as well as researchers for learning and working in the field.

MSC:
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
65-02 Research exposition (monographs, survey articles) pertaining to numerical analysis
65Y15 Packaged methods for numerical algorithms
65-00 General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to numerical analysis
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
35L65 Hyperbolic conservation laws
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