A Five-Step P-Stable Method for the Numerical Integration of Third Order Ordinary Differential Equations

D. O. Awoyemi, S. J. Kayode, L. O. Adoghe

Department of Mathematical Sciences, Federal University of Technology, Akure, Nigeria.
Department of Mathematics, Ambrose Alli University, Ekpoma, Nigeria.
Department of Mathematics, Landmark University, Umuaru, Nigeria.

DOI: 10.4236/ajcm.2014.43011                

Abstract

In this paper we derived a continuous linear multistep method (LMM) with step number k = 5 through collocation and interpolation techniques using power series as basis function for approximate solution. An order nine p-stable scheme is developed which was used to solve the third order initial value problems in ordinary differential equation without first reducing to a system of first order equations. Taylor’s series algorithm of the same order was developed to implement our method. The result obtained compared favourably with existing methods.

Keywords

Continuous Collocation, Multistep Methods, Interpolation, Third Order, Power Series, Approximate Solution

Conflicts of Interest

The authors declare no conflicts of interest.

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