A Six-Step Continuous Multistep Method For The Solution Of General Fourth Order Initial Value Problems Of Ordinary Differential Equations

Abstract

In this paper, continuous Linear Multistep Method (LMM) for the direct solution of fourth order initial value problems in ordinary differential equation is derived. The study provides the use of both collocation and interpolation techniques to obtain the schemes. Direct form of power series is used as basis function for approximation. An order six symmetric and zero-stable method is obtained. To implement our method, predictors of the same order of accuracy as the main method were developed using Taylor’s series algorithm.  This implementation strategy is found to be efficient and more accurate as the result has shown in the numerical experiments. The result obtained confirmed the superiority of our method over existing schemes Keywords: Direct method; Fourth order; interpolation; collocation multistep methods,;power series; approximate solutions.