An effective numerical integration method for typical stiff systems

Abstract

Abstract There is an equivalence between stiff and singularly perturbed systems of ordinary differential equations. This feature is exploited in this paper by numerically employing recent singular perturbation methods to attack troublesome boundary layer stage of the solution in which some variables have very short response times. The numerical method affords a means of essentially determining the thickness of this boundary layer. The algorithm is capable of high stability and accuracy for the commonly occurring stiff system, whether or not it is in singularly perturbed form. Application to a singularly perturbed reaction system and a highly stiff reactor system not in singularly perturbed form demonstrate the effectiveness and utility of this approach.