Numerical Solution of Robin-Dirichlet Problem for a Nonlinear Wave Equation with Memory Term

In this paper, we propose a numerical procedure to find the approximate solution of initial-boundary value problem for a nonlinear wave equation with memory term. First, the local existence and uniqueness is proved by the linear approximating method and the Faedo-Galerkin method. Next, a numerical scheme is constructed by the finite-difference method and the standard arguments of ordinary differential equation. Finally, an example is given to simulate the numerical results of the proposed algorithm.