Higher-order numerical methods for transient wave equations.

*(English)*Zbl 0985.65096
Scientific Computation. Berlin: Springer. xiii, 348 p. (2002).

This is a remarkable book about numerical treatment of wave-type equations in the time domain. It contains as part I, Basic definitions and properties, as part II, Finite difference methods and as part III, Finite element methods. Besides a unified presentation of the topic, new methods (mass-lumped mixed formulations) as well as new results on classical and modern approximation schemes are thoroughly carried out. A special emphasis is laid upon perfectly matched layers when unbounded domains are considered. The book will be of particular interest to mathematicians, physicists and engineers working in academia as well as in industry on the field of numerical analysis of wave-like phenomena.

Reviewer: Calin Ioan Gheorghiu (Cluj-Napoca)

##### 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 |

76-02 | Research exposition (monographs, survey articles) pertaining to fluid mechanics |

78-02 | Research exposition (monographs, survey articles) pertaining to optics and electromagnetic theory |

65M60 | Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs |

76M10 | Finite element methods applied to problems in fluid mechanics |

76M20 | Finite difference methods applied to problems in fluid mechanics |

35L05 | Wave equation |

78M10 | Finite element, Galerkin and related methods applied to problems in optics and electromagnetic theory |

78M20 | Finite difference methods applied to problems in optics and electromagnetic theory |

65M12 | Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs |