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

Year 2019, Volume: 32 Issue: 2, 608 - 614, 01.06.2019

Oluwaseun Adeyeye , Zurni Omar

Abstract

This article introduces two approaches to
develop block methods for solving second order ordinary differential equations
directly. Both approaches, namely a new linear block approach and the modified
Taylor series approach are capable of producing a family of methods that will
simultaneously approximate the solutions of any ordinary differential equation
at the respective grid points of the block method. The computational
complexities of both approaches are examined, and the results show the new
linear block approach require less computations compared to the modified Taylor
series approach.

Keywords

Computational Complexity, New Linear Block, Modified Taylor Series, Block Methods, Second Order ODEs

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