Computational Complexity Comparison of a New Linear Block Approach and Modified Taylor Series Approach for Developing k-Step Third Derivative Block Methods

Abstract

This article introduces two approaches to develop block methods for solving second orderordinary differential equations directly. Both approaches, namely a new linear block approachand the modified Taylor series approach are capable of producing a family of methods that willsimultaneously approximate the solutions of any ordinary differential equation at the respectivegrid points of the block method. The computational complexities of both approaches areexamined, and the results show the new linear block approach require less computationscompared to the modified Taylor series approach.