Convergence analysis of two-stage waveform relaxation method for the initial value problems

We present a class of two-stage waveform relaxation methods for solving the initial value problems of ordinary differential equations. By making use of the Laplace transform we discuss the convergence of these methods, and derive sufficient conditions for guaranteeing their convergence when the system matrices are specifically H-matrices. Also we discuss the monotonicity of the convergence sequence. Further we compare the sequences generated by two different inner splittings of the same initial value problem.