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

Bales, Laurence A.; Dougalis, Vassilios A.; Serbin, Steven M.

doi:10.1090/S0025-5718-1985-0790645-1

Cosine methods for second-order hyperbolic equations with time-dependent coefficients
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by Laurence A. Bales, Vassilios A. Dougalis and Steven M. Serbin PDF

Math. Comp. 45 (1985), 65-89 Request permission

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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