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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.

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
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