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Mathematics of Computation

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Cosine methods for second-order hyperbolic equations with time-dependent coefficients


Authors: Laurence A. Bales, Vassilios A. Dougalis and Steven M. Serbin
Journal: Math. Comp. 45 (1985), 65-89
MSC: Primary 65M05; Secondary 65M60
DOI: https://doi.org/10.1090/S0025-5718-1985-0790645-1
MathSciNet review: 790645
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Abstract: We analyze efficient, high-order accurate methods for the approximation of the solutions of linear, second-order hyperbolic equations with time-dependent coefficients. The methods are based on Galerkin-type discretizations in space and on a class of fourth-order accurate, two-step, cosine time-stepping schemes. Preconditioned iterative techniques are used to solve linear systems with the same operator at each time step. The schemes are supplemented by single-step high-order starting procedures and need no evaluations of derivatives of operators. $ {L^2}$-optimal error estimates are proved throughout.


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DOI: https://doi.org/10.1090/S0025-5718-1985-0790645-1
Article copyright: © Copyright 1985 American Mathematical Society