One Step Five-Point Hybrid Block Method for the Solution of Initial Value Problem for Third Order Ordinary Differential Equation

Adamu M. Alkali; Dahiru Umar; Suleman Timothy; Aisha I. Ahmed

doi:10.4314/cajost.v2i1.39

Authors

Adamu M. Alkali Department of Mathematics, Modibbo Adama University of Technology, Yola, Adamawa State, Nigeria.
Dahiru Umar Department of Mathematics, Modibbo Adama University of Technology, Yola, Adamawa State, Nigeria.
Suleman Timothy Department of Mathematics, Federal College of Education Yola, Adamawa State, Nigeria.
Aisha I. Ahmed Department of Mathematics, Modibbo Adama University of Technology, Yola, Adamawa State, Nigeria.

DOI:

https://doi.org/10.4314/cajost.v2i1.39

Keywords:

collocation, interpolation, power series, hybrid, zero stability

Abstract

A five-point hybrid block method for direct solution of third order initial value
problem of ordinary differential equations (ODEs) is considered. The method is
based on the collocation and interpolation of the power series approximate
solution to generate a continuous linear multistep method. The developed
method is applied to solve some third order ordinary differential equations for
the purpose of comparison with existing methods. It is observed that from the
numerical result obtained, the method is better than the previous methods in
terms of accuracy.