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Some remarks on a class of rational approximations to the cosine

  • Part II Numerical Mathematics
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Abstract

Some previously introduced methods for the numerical solution of second-order evolution equations based on a class of rational approximations to the cosy, y real, with denominators (1+x 2 y 2)s are revisited. It is shown that maximal accuracy occurs for each integers≧1 for a suitable choice of the parameterx. An improved sufficient condition for unconditional stability is obtained. Conditional stability and periodicity of these methods are also studied.

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Authors and Affiliations

  1. Department of Mathematics, University of Tennessee, 37916, Knoxville, Tennessee, USA

    Vassilios A. Dougalis & Steven M. Serbin

Authors
  1. Vassilios A. Dougalis
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  2. Steven M. Serbin
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Additional information

Work supported by USARO Grant DAAG 29-78-C-0024.

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Dougalis, V.A., Serbin, S.M. Some remarks on a class of rational approximations to the cosine. BIT 20, 204–211 (1980). https://doi.org/10.1007/BF01933192

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  • DOI: https://doi.org/10.1007/BF01933192

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