New Generalized Algorithm for Developing  k-Step Higher Derivative Block Methods for Solving Higher Order Ordinary Differential Equations

Oluwaseun Adeyeye; Zurni Omar

doi:10.5614/j.math.fund.sci.2018.50.1.4

Authors

Oluwaseun Adeyeye Department of Mathematics, School of Quantitative Sciences, Universiti Utara Malaysia, Kedah, Malaysia
Zurni Omar Department of Mathematics, School of Quantitative Sciences, Universiti Utara Malaysia, Kedah, Malaysia

DOI:

https://doi.org/10.5614/j.math.fund.sci.2018.50.1.4

Keywords:

block methods, generalized algorithm, higher derivative, higher order, k-step, Taylor series

Abstract

This article presents a new generalized algorithm for developing k-step (m+1)^th derivative block methods for solving m^th order ordinary differential equations. This new algorithm utilizes the concept from the conventional Taylor series approach of developing linear multistep methods. Certain examples are shown to show the simplicity involved in the usage of this new generalized algorithm.

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