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Cosine methods for nonlinear second-order hyperbolic equations


Authors: Laurence A. Bales and Vassilios A. Dougalis
Journal: Math. Comp. 52 (1989), 299-319, S15
MSC: Primary 65M60
DOI: https://doi.org/10.1090/S0025-5718-1989-0955747-9
MathSciNet review: 955747
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Abstract: We construct and analyze efficient, high-order accurate methods for approximating the smooth solutions of a class of nonlinear, second-order hyperbolic equations. The methods are based on Galerkin type discretizations in space and on a class of fourth-order accurate two-step schemes in time generated by rational approximations to the cosine. Extrapolation from previous values in the coefficients of the nonlinear terms and use of preconditioned iterative techniques yield schemes whose implementation requires solving a number of linear systems at each time step with the same operator. $ {L^2}$ optimal-order error estimates are proved.


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DOI: https://doi.org/10.1090/S0025-5718-1989-0955747-9
Article copyright: © Copyright 1989 American Mathematical Society

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