Performance of 4-Point Diagonally Implicit Block Method for Solving Ordinary Differential Equations

Abstract

This paper describes the development of a 4-point diagonally implicit block method for solving first order Ordinary Differential Equations (ODEs) using variable step size. This method will estimate the solutions of Initial Value Problems (IVPs) at four points simultaneously. The method developed is suitable for the numerical integration of non stiff and mildly stiff differential systems. The performances of the 4-point block method are compared in terms of maximum error and total number of steps to the non block method 1PVSO. Keywords: 4-Point; Implicit Block Method; Block Method; Ordinary Differential Equations.