A multirate W-method for electrical networks in state–space formulation

摘要

Subunits of coupled technical systems typically behave on differing time scales, which are often separated by several orders of magnitude. An ordinary integration scheme is limited by the fastest changing component, whereas so-called multirate methods employ an inherent step size for each subsystem to exploit these settings. However, the realization of the coupling terms is crucial for any convergence. Thus the approach to return to one-step methods within the multirate concept is promising. This paper introduces the multirate W-method for ordinary differential equations and gives a theoretical discussion in the context of partitioned Rosenbrock–Wanner methods. Finally, the MATLAB implementation of an embedded scheme of order (3)2 is tested for a multirate version of Prothero–Robinson's equation and the inverter-chain-benchmark.