Difference schemes for non-autonomous stiff systems of ordinary differential equations

Abstract

The properties of Rosenbrock schemes with complex coefficients and implicit Runge-Kutta schemes for the numerical solution of Cauchy problems for stiff systems of ordinary differential equations are investigated. The model problem chosen is a linear non-autonomous system. A one-stage second-order approximation Rosenbrock scheme is constructed, which is monotonic and damped to second order when applied to non-autonomous linear systems. This scheme enables one to compute with large step-size outside the boundary layer and can be used for the numerical solution of a broad range of stiff problems which are nearly linear (including, e.g., computations of transients in electrical circuits).