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Home  >  volume 36 (no1)

One-Step Modified Block Implicit Hybrid Method for Direct Solution of General Fourth Order Ordinary Differential Equations by Duromola M.K and Bolarinwa Bolaji (Pages 31-46)
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The focus of this paper is the developmentof a one-step modifiedblock implicit hybrid method with six off-grid points for direct solution ofinitial value problems (ivps)of general fourth order ordinary differential equations. Power series was adopted as the basis function for the solution of the ivps. An approximate solutionfrom the basis function was interpolated at first grid and some selected off-grid points while the fourth derivative of the approximate solution was collocated at all grid and off-grid points to generate a system of linear equations for the determination of the unknown parameters.

The derived method was tested for consistency, zero stability, convergence and absolute stability. The method was implemented with test problems to confirm its accuracy and usability. Comparison of the results with some existing methods shows superiority ofaccuracy of the new method.

                Keywords: Hybrid, modified block, grid point, off-step points, Interpolation and collocation.

                AMS Subject classification: 65L05, 65L06