Semi-Implicit Runge-Kutta Procedures with Error Estimates for the Numerical Integration of Stiff Systems of Ordinary Differential Equations

Abstract

A -stable, semi-implicit Runge-Kutta procedures requiring at most one Jacobian evaluation per time step are developed for the approximate numerical integration of stiff systems of ordinary differential equations. A simple procedure for estimating the local truncation error is described and, with the help of this estimate, efficient integration procedures are derived. The algorithms are illustrated by direct application to a particular example.