Research Article Open Access

New Hybrid Block Method with Three Off-Step Points for Solving First Order Ordinary Differential Equations

Ra’ft Abdelrahim1, Zurni Omar1 and John Olusola Kuboye1
  • 1 Department of Mathematics, School of Quantitative Sciences, Universiti of Utara Malaysia (UUM), Malaysia

Abstract

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.

American Journal of Applied Sciences
Volume 13 No. 2, 2016, 209-212

DOI: https://doi.org/10.3844/ajassp.2016.209.212

Submitted On: 1 December 2015 Published On: 18 February 2016

How to Cite: Abdelrahim, R., Omar, Z. & Kuboye, J. O. (2016). New Hybrid Block Method with Three Off-Step Points for Solving First Order Ordinary Differential Equations. American Journal of Applied Sciences, 13(2), 209-212. https://doi.org/10.3844/ajassp.2016.209.212

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Keywords

  • Hybrid Block
  • Single-Step
  • Interpolation
  • Collocation
  • Ordinary Differential Equation