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

Abstract

his 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 given to show the simplicity involved in the usage of this new generalized algorithm.

Keywords

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