Error bounds for numerical solutions of ordinary differential equations |
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Authors: | Dr. G. J. Cooper |
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Affiliation: | (1) School of Mathematical and Physical Sciences, University of Sussex, Falmer, BN 1 9 QH Brighton, England |
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Abstract: | 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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