On a High Order Iterative Scheme for a Nonlinear Wave Equation

Abstract

In this paper, a high order iterative scheme is established in order to get a convergent sequence, at a rate of order N, to a local unique weak solution of a nonlinear wave equation associated with homogeneous Dirichlet boundary conditions. This scheme shows that the convergence can be obtained with a high rate if the nonlinear term in the original equation is smooth enough.