Computation of Continuous Approximate Solutions to Ordinary Differential Equations by a Simplification of Picard's Method of Successive Substitutions

Abstract

The computation of continuous approximate solutions of Differential Equations has become increasingly important in order, for instance, to be able to apply error bounding techniques from functional analysis. An efficient procedure for computing continous approximate solutions to initial value problems in ordinary differential equations is presented. The method is a simplification of Picard's method of successive substitutions.