Department of Mathematics
How do elements of semi-discrete systems
affect convergence of waveform relaxation?
Barbara Zubik-Kowal
Boise State University
Waveform relaxation is an iterative method. It has an advantage that it can be applied in parallel computing environments. A further advantage is that implementation of implicit ODE solvers applied to the resulting waveform relaxation schemes is straightforward. No algebraic systems need to be solved in any time step, unlike the situation where waveform relaxation is not applied. These advantages are useful when solving both linear and nonlinear differential systems. We can replace nonlinear systems of ODEs by sequences of linear problems which can be effectively integrated by A(α)-stable backward differentiation methods or A-stable implicit Runge-Kutta methods. This allows for much larger time steps than those used for explicit methods. In this talk we present a new approach to the analysis of convergence of waveform relaxation. In our approach we investigate magnitutes of elements of differential systems. New results about relations between the elements and convergence of waveform relaxation are presented. Our theoretical results are new for both delay and non-delay linear and nonlinear differential equations. The results are confirmed by numerical experiments.
All interested persons are welcome.