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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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