One-step Hybrid Block Method for Directly Solving Fifth-order Initial Value Problems of Ordinary Differential Equations
M. K. Duromola *
Department of Mathematical Sciences, Federal University of Technology, Akure, Nigeria.
A. L. Momoh
Department of Mathematical Sciences, Federal University of Technology, Akure, Nigeria.
J. M. Adeleke
Department of Mathematical Sciences, Federal University of Technology, Akure, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
An effective one-step hybrid block for getting the approximate solution of a fifth-order IVP with applications to problems in the sciences and engineering is constructed in this study. The mathematical formulation of the method is based on the principle of interpolation and collocation of the trial solution and its derivatives at the chosen equidistant grid and off-grid points. The basic properties of the derived method are examined, and it has an order greater than one, zero stable, consistent, and hence convergent. The derived method is applied to solve five different linear and nonlinear fifth-order initial value problems. Comparison of the absolute errors obtained using the derived method with a few existing ones in the literature supports its good performance.
Keywords: Higher-order, interpolation, collocation, grid and off-grid points, zero stability, consistency