A method for the estimation of errors propagated in the numerical solution of a system of ordinary differential equations

Abstract

Let be x′ = f ( t , x ) a system of ordinary differential equations, with initial conditions x ( a ) = s , which is integrated numerically by a finite difference method of order p and constant step h. To estimate the truncation and round-off errors accumulated during the numerical process it is established a method based on the current theory of the asymptotic behaviour (when h →0) of errors. This method should avoid the main difficulties that arise when the results of the theory must be applied to practical cases. The method has been successfully tested and applied to estimate the errors accumulated in a numerical computation of planetary perturbations on the orbit of a comet.