Author(s)

Monday Kolawole Duromola¹, Adelegan Lukuman Momoh¹, Olusegun Mayowa Akinmoladun²

¹Department of Mathematical Sciences, Federal University of Technology, Akure, Nigeria.
²Department of Mathematical Sciences, Lagos State University of Sciences of Technology, Ikoroodu, Nigeria.

This article aims to derive, analyse, and implement an efficient one-step implicit hybrid method with block extension comprised of seven off-step points to directly solve Initial Value Problems (IVPs) of general four-order ordinary differential equations. For the resolution of the fourth-order IVPs, the exact was approximated by a polynomial termed basis function. The partial sum of the basis function and its fourth derivative were interpolated and collocated at some selected grid and off-grid points for the unknown parameters to be determined. The derived method, when tested, is found to be consistent, convergent, and zero-stable. The method’s accuracy and usability were experimented with using specific sample problems, and the findings revealed that it surpassed some cited methods in terms of accuracy.

Implicit, Absolute Stability, Grid Points, Off-Grid Points, Convergence, Interpolation, and Collocation

Duromola, M. , Momoh, A. and Akinmoladun, O. (2022) Block Extension of a Single-Step Hybrid Multistep Method for Directly Solving Fourth-Order Initial Value Problems. American Journal of Computational Mathematics, 12, 355-371. doi: 10.4236/ajcm.2022.124026.