Numerical studies of high-dimensional nonlinear viscous and nonviscous wave equations by using finite difference methods

Abstract

The numerical solutions of two-dimensional (2D) and three-dimensional (3D) nonlinear viscous and nonviscous wave equations via the unified alternating direction implicit (ADI) finite difference methods (FDMs) are obtained in this paper. By making use of the discrete energy method, it is proven that their numerical solutions converge to exact solutions with an order of two in both time and space with respect to [Formula: see text]-norm. Numerical results confirm that they are relatively accurate and high-resolution, and more successfully simulate the conservation of the energy for nonviscous equations, and the dissipation of the energy for viscous equation.