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Sin-Cos-Taylor-Like method for solving stiff ordinary diffrential equations

Ahmad, Rokiah @ Rozita and Yaacob, Nazeeruddin (2005) Sin-Cos-Taylor-Like method for solving stiff ordinary diffrential equations. Journal of Fundamental Sciences, 1 . pp. 34-43. ISSN 1823-626X

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Official URL: http://www.ibnusina.utm.my/jfs/paper/jfs034043.pdf

Abstract

This paper discusses the derivation of an explicit Sin-Cos-Taylor-Like method for solving stiff ordinary differential equations, which is a formulation of the combination of a polynomial and the exponential function. This new method requires extra work to evaluate a number of differentiations of the function involved. However, the result shows smaller errors when compared to the results from the explicit classical fourth-order Runge-Kutta (RK4) and the Adam- Bashforth-Moulton (ABM) methods. Implicit methods could work well for stiff problems but have certain drawbacks especially when discussing about the cost. Although extra work is required, this explicit method has its own advantages. Besides providing excellent results, the cost of computation using this explicit method is much cheaper than the implicit methods. We also considered the stability property for this method since the stability property of the classical explicit fourth order Runge-Kutta method is not adequate for the solution of stiff problems. As a result, we find that this explicit method is of order-6, which has been developed, and proved to be both A-stable and L-stable.

Item Type:Article
Uncontrolled Keywords:Stiff ordinary differential equations, Explicit methods, A-stable, L-stable
Subjects:Q Science > QA Mathematics
Divisions:Science
ID Code:81
Deposited By: Kamariah Mohamed Jong
Deposited On:06 Feb 2007 05:49
Last Modified:01 Jun 2010 02:40

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