The time two-grid algorithm combined with difference scheme for 2D nonlocal nonlinear wave equation

In the paper, we present a time two-grid difference (TGD) method for the approximation of two-dimensional (2D) nonlocal nonlinear wave equation (NNWE). First, the solution is obtained by solving a nonlinear system on the coarse grid (CG), then by using the numerical solutions obtained on the CG we construct a linearized system on the fine grid (FG). Meanwhile the auxiliary values calculated by Lagrange linear interpolation formula. Further, we prove the existence and uniqueness of solution on the CG and FG. Also the stability and convergence is proved strictly through the energy analysis scheme. Finally, two numerical examples are shown, which verify the proposed TGD method is more efficient than the general finite difference (GFD) method.