An accelerated Newton method of high-order convergence for solving a class of weakly nonlinear complementarity problems

In this paper, by extending the classical Newton method, we investigate an accelerated Newton iteration method (ANIM) with high-order convergence for solving a class of weakly nonlinear complementarity problems which arise from the discretization of free boundary problems. Theoretically, the performance of high-order convergence is analyzed in details. Some numerical experiments demonstrate the efficiency of the presented method.