Two Level Nonlinear Conservative Difference Scheme for Solving Generalized BBM-Burgers Equation

In this paper, a two level nonlinear Crank-Nicolson difference scheme is proposed. The scheme provides a numerical solution to the initial boundary value problem of general BBM-Burgers equation. A conservative variable of the equation is simulated well with the scheme. In the simulation, the prior estimate and uniqueness of the solution are also obtained. In addition, the second order convergence and unconditional stability are proved by using energy analysis.