A Novel Multiderivative Hybrid Method for the Numerical Treatment of Higher Order Ordinary Differential Equations

O. E. Abolarin, E. O. Adeyefa , J. O. Kuboye; and B. G. Ogunware

Abstract

This work examines the direct solution of higher order (second, third and fourth order) initial value problem (IVP) of ordinary differential equations (ODEs) by hybrid method. The method was derived using collocation and interpolation technique where the use of power series as an approximate solution is considered. A two step with two off-step hybrid linear multistep method that gives solution to second, third and fourth order initial value problem of ordinary differential equations is developed. Block method is used to generate the independent solution at selected grid and off grid points. The properties of the method are properly investigated. The numerical results generated when the new method is applied to higher order ODEs compared favourably with existing methods in terms of accuracy. The developed method takes away the burden of developing separate method for the solution of each of second, third and fourth order initial value problem of ordinary differential equations.

Keywords

Hybrid; Block Method; Collocation; Interpolation; Higher Order Ordinary Differential Equations and Power series.