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Application to differential transformation method for solving systems of differential equations
Faculty
Science
Year:
2008
Type of Publication:
Article
Pages:
2552-2559
Authors:
Hassan, I. H. Abdel-Halim
DOI:
10.1016/j.apm.2007.09.025
Journal:
APPLIED MATHEMATICAL MODELLING ELSEVIER SCIENCE INC
Volume:
32
Research Area:
Engineering; Mathematics; Mechanics
ISSN
ISI:000259785500007
Keywords :
systems of differential equations, stiff differential system, differential transformation, Taylor's series expansion, Runge-Kutta method
Abstract:
In this paper, we present an analytical solution for different systems of differential equations by using the differential transformation method. The convergence of this method has been discussed with some examples which are presented to show the ability of the method for linear and non-linear systems of differential equations. We begin by showing how the differential transformation method applies to a non-linear system of differential equations and give two examples to illustrate the sufficiency of the method for linear and non-linear stiff systems of differential equations. The results obtained are in good agreement with the exact solution and Runge-Kutta method. These results show that the technique introduced here is accurate and easy to apply. (C) 2007 Elsevier Inc. All rights reserved.
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