Review of Numerical Integration Techniques for Stiff Ordinary Differential Equations

Abstract

Ordinary differential equations with widely separated eigenvalues (stiff O.D.E.) occur often in practice and present severe numerical integration problems. The stability and accuracy problems associated with the numerical solution of such equations are outlined. Several methods, including a modified Runge-Kutta method due to Treanor, a class of implicit Runge-Kutta methods, extrapolation methods, and methods based on the inclusion of second derivatives and exponential fitting, are considered. Numerical results are given on three stiff systems for stiff and conventional methods and recommendations are made on what methods to use for particular systems.

Additional details