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