ROW methods adapted to a cheap Jacobian Original Research Article

Many packages for time domain simulation of electric circuits supply the Jacobian with every function evaluation at very low additional costs. In Rosenbrock–Wanner methods, the cheap Jacobian information can be used at each stage to introduce additional method coefficients which allow for a given order of convergence with first less stages or secondly less function evaluations per integration step. The first approach has been discussed by Günther and Hoschek (1997). In this paper we concentrate on the latter approach and derive the order conditions by Butcher series. Finally, numerical results for the inverter chain are discussed for an embedded method of order (3)4 with four stages and only two combined function and Jacobian evaluations.