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On the design of high order exponentially fitted formulae for the numerical integration of stiff systems

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Summary

Single step exponentially fitted integration formulae of orders 4 and 6 are derived. The final approximation to the required solution is obtained via a linear combination of asymptotically less accurate solutions obtained using conventional implicit integration formulae. This linear combination is performed in such a way that the final integration formula, as well as having an increased order of accuracy, integrates a certain pre-determined ordinary differential equation exactly. The algorithms developed are illustrated by means of some numerical examples.

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  1. Dept. 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 the design of high order exponentially fitted formulae for the numerical integration of stiff systems. Numer. Math. 36, 253–266 (1980). https://doi.org/10.1007/BF01396654

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  • DOI: https://doi.org/10.1007/BF01396654

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