IJPAM: Volume 109, No. 4 (2016)

DIRECT SOLUTION OF FOURTH ORDER ORDINARY
DIFFERENTIAL EQUATIONS USING A ONE STEP
HYBRID BLOCK METHOD OF ORDER FIVE

Zurni Omar$^1$, Ra'ft Abdelrahim$^2$
$^{1,2}$Department of Mathematics
School of Quantitative Sciences
College of Art and Sciences
Univeristi Utara Malaysia
Kedah, MALAYSIA
rafatshaab@yahoo.com

Abstract. In this article, a power series of order eight is adopted as a basis function to develop one step hybrid block method with three off step points for solving general fourth order ordinary differential equations. The strategy is employed for the developing this method are interpolating the power series at $x_n $ and all off-step points and collocating its fourth derivative at all points in the selected interval. The method derived is proven to be consistent, zero stable and convergent with order five. Taylor’s series is used to supply the starting values for the implementation of the method while the performance of the method is tasted by solving linear and non-linear problems.

Received: February 20, 2016

Revised: August 11, 2016

Published: October 9, 2016

AMS Subject Classification: 65L05, 65L06, 65L20

Key Words and Phrases: hybrid method, block method, fourth order differential equation, power series, three off step points
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DOI: 10.12732/ijpam.v109i4.1 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: 2016
Volume: 109
Issue: 4
Pages: 763 - 777


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