IJPAM: Volume 81, No. 6 (2012)

A FOURTH ORDER A-STABLE EXPLICIT ONE-STEP
METHOD FOR SOLVING STIFF DIFFERENTIAL
SYSTEMS ARISING IN CHEMICAL REACTIONS

A.M.N. Ebady$^1$, H.M. Habib$^2$, E.R. El-Zahar$^3$
Department of Mathematics
College of Sciences and Humanities
Salman Bin Abdulaziz University
P.O. Box 83, Alkharj 11942, KSA


Abstract. In this paper, a new A-stable explicit one-step integration method is developed for numerically solving stiff differential systems which characterize several kinds of linear reactions and diffusion from biochemistry, physiology, etc. The method is based on deriving a nonlinear relation between the dependent variable and its derivatives from the well known Taylor expansion. The method can be classified as a rational method. The accuracy and stability properties of the method are investigated and shown to yield at least fourth-order and A-stable. Some differential systems arising in chemical reactions will be solved to illustrate the performance and accuracy of the method.

Received: April 3, 2012

AMS Subject Classification: 65L05

Key Words and Phrases: stiff problems, initial-value problems, explicit methods

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2012
Volume: 81
Issue: 6