Implementation of Rosenbrock Methods

Abstract

Rosenbrock formulas have shown promise in research codes for the solution of initial value problems for stiff systems of ordinary differential equations (ODEs). To help assess their practical value, the author wrote an item of mathematical software based on one such formula. This required a varmty of algomthmic and software developments Those of general interest are reported in this paper Among them is a way to select automatically, at every step, an exphcit Runge-Kutta formula or a Rosenbrock formula according to the stiffness of the problem. Solving linear systems is important to methods for stiff ODEs and is rather special for Rosenbrock methods. A cheap, effective estimate of the condition of the linear systems is derived. Some numerical results are presented to illustrate the developments.