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Error bounds for numerical solutions of ordinary differential equations

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Summary

An a posteriori error bound, for an approximate solution of a system of ordinary differential equations, is derived as the solution of a Riccati equation. The coefficients of the Riccati equation depend on an eigenvalue of a matrix related to a Jacobian matrix, on a Lipschitz constant for the Jacobian matrix, and on the approximation defect. An upper bound is computable as the formal solution of a sequence of Riccati equations with constant coefficients. This upper bound may sometimes be used to control step length in a numerical method.

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  1. School of Mathematical and Physical Sciences, University of Sussex, Falmer, BN 1 9 QH, Brighton, England

    G. J. Cooper

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  1. G. J. Cooper
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Cooper, G.J. Error bounds for numerical solutions of ordinary differential equations. Numer. Math. 18, 162–170 (1971). https://doi.org/10.1007/BF01436325

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  • DOI: https://doi.org/10.1007/BF01436325

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