On the L∞-convergence of two conservative finite difference schemes for fourth-order nonlinear strain wave equations

In this article, numerical solutions for the two-dimensional fourth-order nonlinear strain wave equations are considered using two finite difference schemes. The proposed difference schemes guarantee the conservation of discrete energy. Existence of difference solutions is shown using Brouwer's fixed point theorem. The uniqueness and the stability are derived by means of the discrete energy. A second-order convergence is proved in discrete L-infinity-norm. Some numerical experiments are given to validate the theoretical results.