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

DOI: 10.4236/oalib.1102667, PP. 1-14

Subject Areas: Ordinary Differential Equation

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

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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.

Cite this paper

Duromola, M. K. (2016). An Accurate Five Off-Step Points Implicit Block Method for Direct Solution of Fourth Order Differential Equations. Open Access Library Journal, 3, e2667. doi: http://dx.doi.org/10.4236/oalib.1102667.

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