Convergence of waveform relaxation methods for Hermitian positive definite linear systems

This paper studies the multi-splitting algorithm and the two-stage iterative method for waveform relaxation (WR) method, solving the initial value problems for linear systems of ordinary differential equations (ODEs) in the form y′(t)+Ay(t)=f(t). Convergence of both cases are analyzed when the coefficient matrix is Hermitian positive definite and the splittings are P-regular. Finally, numerical experiment is presented.