Abstract
In this paper, we propose two finite difference schemes to solve a class of a fourth-order strongly damped nonlinear wave equation in two dimensions. We prove some a priori bounds and establish the second order convergence in L∞−norm for the difference solutions. We also discuss the stability and the unique solvability of the two proposed difference schemes. Finally, we provide numerical examples to validate the order of convergence, unconditional stability and the nonincreasing discrete energy in time for the two introduced schemes.