IJPAM: Volume 92, No. 1 (2014)

BLOCK NUMERICAL INTEGRATOR FOR THE SOLUTION
OF $y^{^{\prime \prime \prime }}=f(x,y,y^{\prime },y^{\prime \prime })$

Fasasi M. Kolawole$^1$, A. Olaide Adesanya$^2$, S.O. Adee$^3$
$^{1,2,3}$Department of Mathematics
Modibbo Adama University of Technology
Yola, Adamawa State, NIGERIA


Abstract. A block method for solution of third order initial value problems of ordinary differential equations is presented in this paper. The scheme was derived using collocation and interpolation approach to generate a continuous linear multistep method which was solved for the independent solution to give a continuous block method. The result was evaluated at selected grid points to give a discrete block which gave simultaneous solutions at both grid and off grid points. The stability and convergence of the method were investigated, and found to be A -stable with good region of absolute stability. The accuracy of the block method was established numerically after comparing it with the existing method.

Received: December 13, 2013

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

Key Words and Phrases: collocation, hybrid points, independent solution, interpolation, zero stable, consistent, convergent

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DOI: 10.12732/ijpam.v92i1.7 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: 1
Pages: 87 - 97

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