A conservative linear difference scheme for the 2D regularized long-wave equation

摘要

In the present work, a three-level in time linear and conservative implicit finite difference scheme for solving the 2D regularized long-wave equation is proposed. The existence, uniqueness, and conservations for mass and energy of the numerical solution are proved by the discrete energy method. The new scheme is shown to be second-order convergent and unconditionally stable. Numerical examples are provided to show the present scheme to be efficient and reliable.