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On improving the absolute stability of local extrapolation

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Summary

A widely used technique for improving the accuracy of solutions of initial value problems in ordinary differential equations is local extrapolation. It is well known, however, that when using methods appropriate for solving stiff systems of ODES, the stability of the method can be seriously degraded if local extrapolation is employed. This is due to the fact that performing local extrapolation on a low order method is equivalent to using a higher order formula and this high order formula may not be suitable for solving stiff systems. In the present paper a general approach is proposed whereby the correction term added on in the process of local extrapolation is in a sense a rational, rather than a polynomial, function. This approach allows high order formulae with bounded growth functions to be developed. As an example we derive anA-stable rational correction algorithm based on the trapezoidal rule. This new algorithm is found to be efficient when low accuracy is requested (say a relative accuracy of about 1%) and its performance is compared with that of the more familiar Richardson extrapolation method on a large set of stiff test problems.

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  1. Department of Mathematics, Imperial College, South Kensington, S.W. 7., London, England

    J. R. Cash

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  1. J. R. Cash
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Cash, J.R. On improving the absolute stability of local extrapolation. Numer. Math. 40, 329–337 (1982). https://doi.org/10.1007/BF01396450

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