TITLE:
A Proof of the Non-Singularity of the D Matrix Used in Deriving the Two—Step Butcher’s Hybrid Scheme for the Solution of Initial Value Problems
AUTHORS:
R. O. Akinola, K. J. Ajibade
KEYWORDS:
Linear Multistep Methods, Non-Singularity, Interpolation and Collocation
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.9 No.12,
December
29,
2021
ABSTRACT: In this paper, we state and prove the conditions for the non-singularity of the D matrix used in deriving the continuous form of the Two-step Butcher’s hybrid scheme and from it the discrete forms are deduced. We also show that the discrete scheme gives outstanding results for the solution of stiff and non-stiff initial value problems than the 5th order Butcher’s algorithm in predictor-corrector form.