Comparing Numerical Methods for the Solution of Stiff Systems of ODEs Arising in Chemistry

Abstract

In chemical applications, one often encounters systems of ordinary differential equations which, although mathematically well-conditioned, are virtually impossible to solve with traditional numerical methods because of the severe stepsize constraint imposed by numerical stability. These stiff equations can be characterized by the presence of transient components, which, although negligible relative to the other components of the numerical solution, constrain the stepsize of traditional numerical methods to be of the order of the smallest time constant of the problem. The chapter describes the comparisons that have been performed at Toronto, and it outlines a new testing program, which is then used to assess the performance of numerical methods in the solution of some stiff ordinary differential equations arising in chemistry. It presents the results of those tests and few specific recommendations. Of the five types of methods tested, only two based on backward differentiation formulas (DIFSUB, GEAR.REV3 and EPISODE) and one based on second derivative multistep formulas (SDBASIC), are suitable as general purpose methods for stiff equations that arise in chemistry.