American Journal of Applied Sciences

Hybrid Block Method for Direct Numerical Approximation of Second Order Initial Value Problems Using Taylor Series Expansions

Oluwaseun Adeyeye and Zurni Omar

DOI : 10.3844/ajassp.2017.309.315

American Journal of Applied Sciences

Volume 14, Issue 2

Pages 309-315

Abstract

In this article, a hybrid block method is utilized for the numerical approximation of second order Initial Value Problems (IVPs). The rigor of reduction to a system of first order initial value problems is bypassed as the hybrid block method directly solves the second order IVPs. Likewise, the methodology utilized also avoids the cumbersome steps involved in the widely adopted interpolation approach for developing hybrid block methods as a simple and easy to implement algorithm using the knowledge from the conventional Taylor series expansions with less cumbersome steps is introduced. To further justify the usability of this hybrid block method, the basic properties which will infer convergence when adopted to solve differential equations are investigated. The hybrid block method validates its superiority over existing methods as seen in the improved accuracy when solving the considered numerical examples.

Copyright

© 2017 Oluwaseun Adeyeye and Zurni Omar. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.