Abstract:
The longitudinal waveform relaxation (WR) proposed by Gander and Ruehli converges faster than the classical WR method. For the former, a free parameter α is contained, wh...Show MoreMetadata
Abstract:
The longitudinal waveform relaxation (WR) proposed by Gander and Ruehli converges faster than the classical WR method. For the former, a free parameter α is contained, which has a significant effect on the convergence rate. The optimization of this parameter is thus an important issue in practice. Here, we apply this new WR method to the fractional-order RC circuits, and optimize such a parameter at the continuous and discrete levels (this gives two parameters αoptc and αoptd). We consider three simple but widely used convolution quadrature for discretization, based on the implicit-Euler method, the two-step backward difference formula, and the trapezoidal rule, and we derive the parameter αoptd for each quadrature. Interestingly, it is found that for the former two quadratures, the optimized parameter αoptd results in a much better convergence rate than αoptc, while for the quadrature based on the trapezoidal rule, αoptd and αoptc result in the same convergence rate.
Published in: IEEE Transactions on Circuits and Systems I: Regular Papers ( Volume: 64, Issue: 7, July 2017)