IJPAM: Volume 92, No. 3 (2014)

A NEW BLOCK NUMERICAL INTEGRATOR FOR
THE SOLVING $y^{^{\prime\prime}}=f(x,y,y^{\prime })$

M. Kolawole Fasasi$^1$, A. Olaide Adesanya$^2$, A.A. Momoh$^3$, M.I. Modebei$^4$
$^{1,2,3}$Department of Mathematics
Modibbo Adama University of Technology
Yola, Adamawa State, NIGERIA
$^4$Department of Mathematics Programme
National Mathematical Centre
Abuja, NIGERIA


Abstract. In this paper, a new block numerical integrator for solving second order initial value problems (IVP) of ordinary differential equations (ODEs) is proposed. The method was derived using interpolation and collocation of power series approximate solution to generate a continuous hybrid linear multistep method which was later solved at independent grid point to give discrete hybrid block method. The analysis of the basic properties of the method shows that the scheme is consistent, convergent and zero stable. Numerical experimentations and comparative analysis with existing methods show that our scheme is efficient.

Received: December 13, 2013

AMS Subject Classification: 65L05, 65L06, 65D30

Key Words and Phrases: collocation, interpolation, Zero stable, consistent, convergent, efficient, hybrid block method

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DOI: 10.12732/ijpam.v92i3.9 How to cite this paper?

Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2014
Volume: 92
Issue: 3
Pages: 421 - 432

CC BY This work is licensed under the Creative Commons Attribution International License (CC BY).