Abstract
This paper advances a procedure to compute the a-posteriori error bounds for the solution of a wide class of ordinary differential equations with given initial conditions. The method is based on an iterative scheme which yields upper and lower bounds which approach each other. The convergence of these iterations is proved analytically. Application of the proposed method is demonstrated by several examples. The method is independent of the integration scheme used. Also, separate bounds for each component of the solution are specifically available as a function of time compared to the bound on the norm yielded by conventional methods.
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