On a high-order iteration technique for a wave equation with nonlinear viscoelastic term

Abstract

In this paper, a high-order iterative technique for solving a wave equation with strong damping and nonlinear viscoelastic term is constructed. For this purpose, we adapt the high-order iterative method used in the earlier works and establish the existence theorem of a recurrent sequence associated with the proposed problem. Thereafter, we prove a N-order convergence of the obtained sequence to a unique solution of the problem.