TITLE:
Block Extension of a Single-Step Hybrid Multistep Method for Directly Solving Fourth-Order Initial Value Problems
AUTHORS:
Monday Kolawole Duromola, Adelegan Lukuman Momoh, Olusegun Mayowa Akinmoladun
KEYWORDS:
Implicit, Absolute Stability, Grid Points, Off-Grid Points, Convergence, Interpolation, and Collocation
JOURNAL NAME:
American Journal of Computational Mathematics,
Vol.12 No.4,
December
27,
2022
ABSTRACT: 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.