Newton waveform relaxation method for solving algebraic nonlinear equations (Q945285)

For solving a nonlinear algebraic system the authors propose a new iterative method, called Newton waveform relaxation method. Starting by a similar way as using the continuous time waveform relaxation iteration for solving differential systems, for solving nonlinear algebraic systems the authors have chosen a splitting function that satisfies a consistency condition and a continuous-time waveform relaxation iteration is attached. The classical Newton's method is then applied to obtain the Newton waveform relaxation method. The advantage of this method is that the splitting function can be chosen broadly. Supposing that the splitting function is Fréchet differentiable with respect to the second argument, the convergence of the Newton waveform relaxation method is proved. Two numerical examples are performed.