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

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)

Journal of Mathematical and Fundamental Sciences
Vol. 50 No. 1 (2018)

This article presents a new generalized algorithm for developing k-step (m+1)th derivative block methods for solving mth 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.