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ISSN:2394-3661 | Crossref DOI | SJIF: 5.138 | PIF: 3.854

International Journal of Engineering and Applied Sciences

(An ISO 9001:2008 Certified Online and Print Journal)

A Class of One-Step Hybrid Third derivative Block Method for the Direct Solution of Initial Value Problems of Second-order Ordinary Differential Equations

( Volume 5 Issue 1,January 2018 ) OPEN ACCESS
Author(s):

Skwame Y., Raymond D.

Abstract:

In this paper, we consider the development of a class of one-step hybrid third derivative block method with three off-grid points for the direct solution of initial value problems of second order Ordinary Differential Equations. We adopted method of interpolation and collocation of power series approximate solution to generate the continuous hybrid linear multistep method, which was evaluated at grid points to give a contnuous block method. The discrete block method was recovered when the continuous block method was evaluated at selected grid points. The basic propertise of the method was investigated and was found to be zero-stable, consistent and convergent. The efficiency of the method was tested on some stiff equations and was found to give better approximation than the existing method, which we compared our result with.

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