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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2024 MCQ for Mathematics of Computation is 1.78.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Cosine methods for nonlinear second-order hyperbolic equations
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by Laurence A. Bales and Vassilios A. Dougalis PDF
Math. Comp. 52 (1989), 299-319 Request permission

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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Additional Information
  • © Copyright 1989 American Mathematical Society
  • Journal: Math. Comp. 52 (1989), 299-319
  • MSC: Primary 65M60
  • DOI: https://doi.org/10.1090/S0025-5718-1989-0955747-9
  • MathSciNet review: 955747