IJPAM: Volume 81, No. 6 (2012)
METHOD FOR SOLVING STIFF DIFFERENTIAL
SYSTEMS ARISING IN CHEMICAL REACTIONS



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