Author(s)

R. O. Akinola^1*, K. J. Ajibade²

¹Department of Mathematics, Faculty of Natural Sciences, University of Jos, Jos, Nigeria.
²Department of Mathematics and Statistics, Concordia University, Montreal, Canada.

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 5^th order Butcher’s algorithm in predictor-corrector form.

Linear Multistep Methods, Non-Singularity, Interpolation and Collocation

Akinola, R. and Ajibade, K. (2021) 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. Journal of Applied Mathematics and Physics, 9, 3177-3201. doi: 10.4236/jamp.2021.912208.