An Accurate Five Off-Step Points Implicit Block Method for Direct Solution of Fourth Order Differential Equations - Open Access Library Journal

OALibJ > Vol.3 No.6, June 2016

An Accurate Five Off-Step Points Implicit Block Method for Direct Solution of Fourth Order Differential Equations ()

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DOI: 10.4236/oalib.1102667 1,128 Downloads 2,214 Views Citations

Author(s)

Monday Kolawole Duromola

Affiliation(s)

Department of Mathematical Sciences, Federal University of Technology, Akure, Nigeria.

ABSTRACT

In this article, my focus is the derivation, analysis and implementation of a new modified one-step implicit hybrid block method with five off-step points. The derived method is to solve directly initial value problems of fourth order ordinary differential equations. The approach for the derivation of the method is to interpolate the approximate power series solution to the problem and to collocate its fourth derivative at the grid and off-grid points to generate systems of linear equations for the determination of the unknown parameters. The derived method is tested for consistency, zero stability, convergence and absolute stability. Accuracy and usability of the method are determined with some test problems and the results obtained are found to be better in accuracy than some existing methods.

KEYWORDS

Interpolation, Continuous Coefficients, Block Method, Numerical Integration, Fourth Order Ordinary Differential Equations

Share and Cite:

Duromola, M. (2016) An Accurate Five Off-Step Points Implicit Block Method for Direct Solution of Fourth Order Differential Equations. Open Access Library Journal, 3, 1-14. doi: 10.4236/oalib.1102667.

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