A six-step Block Unification Integrator for Numerical Solution of Fourth Order Boundary Value Problems

Volume 5, Issue 2, Article 2 - 2018

Authors: Mark I. Modebei ; Raphael B. Adeniyi

Copyright © 2018 . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

 Download PDF File

 Share on GOOGLE+  Share on Twitter  Share on LinkedIn Open XML File

Abstract

In this paper, a new 7th order continuous finite difference methods is proposed. These methods are derived using the Chebyshev polynomials as basis functions. The collocation approach is employed to obtain the main methods and additional methods used for solving general nonlinear fourth order two and four-points boundary value problems. Several numerical examples are shown to illustrate the strength of the method. To show the robustness of this method for high accuracy, we applied the method of line to discretize PDEs into system of fourth order ODEs and thus use the derived method to obtain approximate solution for the PDEs. The approximate solution obtained using the proposed methods is compared to the exact solutions of the problem, and other methods from existing literature. The Convergence of these methods is also guaranteed.

How To Cite This Article

@article{Modebei_2018, doi = {10.31559/glm2018.5.2.2}, url = {https://doi.org/10.31559%2Fglm2018.5.2.2}, year = 2018, publisher = {Refaad for Studies and Research}, volume = {5}, number = {2}, pages = {71--83}, author = {Mark I. Modebei and Raphael B. Adeniyi}, title = {A six-step Block Unification Integrator for Numerical Solution of Fourth Order Boundary Value Problems}, journal = {General Letters in Mathematics} }
Modebei, M. I., & Adeniyi, R. B. (2018). A six-step Block Unification Integrator for Numerical Solution of Fourth Order Boundary Value Problems. General Letters in Mathematics, 5(2), 71–83. doi:10.31559/glm2018.5.2.2
[1]M. I. Modebei and R. B. Adeniyi, “A six-step Block Unification Integrator for Numerical Solution of Fourth Order Boundary Value Problems,” General Letters in Mathematics, vol. 5, no. 2, pp. 71–83, 2018.
Modebei, Mark I., and Raphael B. Adeniyi. “A Six-Step Block Unification Integrator for Numerical Solution of Fourth Order Boundary Value Problems.” General Letters in Mathematics 5, no. 2 (2018): 71–83. doi:10.31559/glm2018.5.2.2.