Convergence properties of waveform relaxation‐newton method

This paper shows the following properties for the waveform relaxation‐Newton method: (1) the iterative solution converges uniformly and globally under the same condition as the convergence condition for the waveform relaxation method; (2) the waveform Newton method used in the inner loop of the iteration converges locally with the second‐order; (3) the waveform relaxation‐Newton method is slower in the convergence both globally and locally than the waveform relaxation method; (4) the time interval where the error monotone decreases is shorter in the waveform relaxation‐Newton method than in the waveform relaxation method; and (5) the convergence speed asymptotically approaches that of the waveform relaxation method.