Hybrid Block Scheme for the Solution of Fifth – Order Initial Value Problems in Ordinary Differential Equations
DOI:
https://doi.org/10.62054/Abstract
This study proposes a novel hybrid block scheme for the direct solution of fifth – order ordinary differential equations (ODEs) with initial conditions, thereby eliminating the computational burden associated with reduction to systems of first – order equations. Power series was used as the basis function for the development of the method. The approximate solution was obtained from the basis function and interpolated at some selected grid points. The fifth derivative of the approximate solution was collocated at all the grid points. This system was solved to determine the unknown parameters in the equations. The values of these parameters were substituted into the basis function to give a One – Step method with continuous coefficients. The discrete schemes obtained from the continuous method and its first, second, third and fourth derivatives were combined and implemented as a block method. The properties of the method were examined. The method was found to be zero stable, consistent and convergent. The method was tested with linear and nonlinear fifth – order problems to confirm its accuracy. Numerical results from this test revealed the method is efficient and it compares favourably with existing methods in the literature.
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Copyright (c) 2026 Fayose F. Ololade, Ogunrinde, R. Bosede, Akinbo, Y. Razaki, Fayose, S. Taiwo (Author)
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