Abstract
Some bounds on the global error of the numerical solution of the initial value problem for a system of ordinary differential equations (ODEs) are developed that show the behavior with respect to the local error tolerance. Problems with solutions that are not smooth at a few points are considered. It is shown how to do local extrapolation with the backward differentiation formulas. An error criterion is proposed that has most of the advantages of both error per step and error per unit step.
This work was partially supported by the Applied Mathematical Sciences program of the Office of Energy Research under DOE grant DE-FG05-86ER25024.
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© 1989 Springer-Verlag
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Shampine, L.F. (1989). Tolerance proportionality in ODE codes. In: Bellen, A., Gear, C.W., Russo, E. (eds) Numerical Methods for Ordinary Differential Equations. Lecture Notes in Mathematics, vol 1386. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0089235
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DOI: https://doi.org/10.1007/BFb0089235
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