Error bounds for numerical solutions of ordinary differential equations

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.