Global Error Estimation in Adams PC-Codes

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Abstract
Efficient and asymptotically (h --, 0) correct global error estimation procedures for initial value problem ODE-codes may be based on a suitable version of defect correction. An implementation of such a procedure for a variable order, variable step Adams PECE-code (typically STEP of Shampme) is described; the global error vector is produced simultaneously with the solution vector at each output point which need not be a grid point. The results of extensive experimentation are presented and d~scussed; m these tests, the qualitative and quantitative behavior of the true error was correctly reflected by the numerical estnnates throughout.

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