Convergence of discrete time waveform relaxation methods

摘要

This paper concerns the discrete time waveform relaxation (DWR) methods for ordinary differential equations (ODEs). We present a general algorithm of constructing the DWR methods with any order of convergence, which applies any numerical methods of ODEs to the perturbed equations of iterative schemes of continuous time waveform relaxation methods. It is demonstrated that the DWR method presented in this paper has the same convergent order as the numerical method used to discretize perturbed equations. Two classes of interpolation polynomials are given to generate perturbed equations. Finally, numerical experiments are presented in order to check against results obtained.