ON DYNAMIC ITERATION METHODS FOR SOLVING TIME-PERIODIC DIFFERENTIAL-EQUATIONS

Dynamic iteration or, more popularly, waveform relaxation has received a great deal of attention as an efficient parallel method for solving large systems of ordinary differential equations of initial value type. By using a multigrid acceleration the method has been applied successfully to parabolic initial boundary value problems. In this paper the applicability of the method is further extended to incorporate the class of time-periodic ordinary and partial differential equations. The authors discuss the convergence characteristics of both the continuous-time and the discrete-time time-periodic iteration. The efficacy of the new procedure is illustrated by an example.