New Hybrid Block Method with Three Off-Step Points for Solving First Order Ordinary Differential Equations
Raâft Abdelrahim, Zurni Omar and John Olusola Kuboye
DOI : 10.3844/ajassp.2016.209.212
American Journal of Applied Sciences
Volume 13, Issue 2
A new single-step hybrid block method with three off-step points for the solution of first order ordinary differential equations is proposed. The strategy employed to develop this method is interpolating the power series approximate solution at xn and off-step points and collocating the derivative of the power at xn+1. The class of linear multistep method derived is then simultaneously applied to first order ordinary differential equations together with the associated initial conditions. The numerical results generated are found to be better when compared with the existing methods in terms of error. Besides its excellent performance in term of accuracy, this method also possesses good properties of numerical method such as zero-stable, consistent and convergent.
© 2016 Raâft Abdelrahim, Zurni Omar and John Olusola Kuboye. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.