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




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

KEYWORDS

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

Cite this paper

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.





Author: Monday Kolawole Duromola

Source: http://www.scirp.org/



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