On a high order iterative scheme for a nonlinear wave equation with the source term containing a nonlinear integral

Abstract

In this paper, we consider the initial and boundary value problem for a nonlinear wave equation, with the source term containing a nonlinear integral, associated with homo- geneous Dirichlet boundary conditions. We establish here a high order iterative scheme in order to get a convergent sequence at a rate of order N to a local unique weak solution of the above problem. This scheme shows that the convergence can be obtained with a high rate if the nonlinear term in the original equation is smooth enough.