Summary
A class of approximation schemes of arbitrary accuracy, generated by a two-step recurrence relation, is devised for evolution equations of the second order. The schemes are effected via a specially constructed family of rational approximations to cos τ for τ≧0 and yield computationally efficient methods for systems of second-order ordinary differential equations and semidiscrete approximations for initial-boundary value problems for second-order hyperbolic equations.
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References
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Research supported by ONR grant N00014-57-A-0298-0015
Research supported by USARO grant DAAG 29-278-C-0024
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Baker, G.A., Dougalis, V.A. & Serbin, S.M. An approximation theorem for second-order evolution equations. Numer. Math. 35, 127–142 (1980). https://doi.org/10.1007/BF01396311
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DOI: https://doi.org/10.1007/BF01396311