A Comparative Study of one-step Methods for Numerical Solution of Initial- Value Problems in Ordinary Differential Equations

Abstract

The ultimate aim of the field of Numerical Analysis is to provide a reliable and convenient methods for obtaining useful solutions to mathematical problems and for extracting useful information from available solutions which are not expressed in proper form. It is a common norm that analytic solutions, when available may be very precise in themselves but may be, of course, of unacceptable form because of the fact that they are not amenable to direct interpretation in numerical terms. In which case numerical analyst may attempt to devise a method of effecting that interpretation in a satisfactory way, or he may prefer to base his analysis instead upon the original formulation.