Conservative finite difference scheme for the nonlinear fourth-order wave equation

Abstract

A conservative finite difference scheme is presented for solving the two-dimensional fourth-order nonlinear wave equation. The existence of the numerical solution of the finite difference scheme is proved by Brouwer fixed point theorem. With the aid of the fact that the discrete energy is conserved, the finite difference solution is proved to be bounded in the discrete L∞−norm. Then, the difference solution is shown to be second order convergent in the discrete L∞−norm. A numerical example shows the efficiency of the proposed scheme.