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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.

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.

Reviewer: Michael SchĂ¤fer (Darmstadt)

### 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 |