General Letters in Mathematics

Volume 5 - Issue 2 (2) | PP: 71 - 83 Language : English
DOI : https://doi.org/10.31559/glm2018.5.2.2
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A six-step Block Unification Integrator for Numerical Solution of Fourth Order Boundary Value Problems

Mark I. Modebei ,
Raphael B. Adeniyi
Received Date Revised Date Accepted Date Publication Date
15/12/2018 2/1/2019 18/1/2019 4/4/2019
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
, M. I. M. & Adeniyi , R. B. (2019). A six-step Block Unification Integrator for Numerical Solution of Fourth Order Boundary Value Problems . General Letters in Mathematics, 5 (2), 71-83, 10.31559/glm2018.5.2.2

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