Conservative Finite Difference Method for Solving Generalized BBM-KdV Equation - WANG Xi; ZHANG Shuang; HU Jin-song (Journal of Harbin University of Science and Technology)
The BBM-KdV equation plays an important role because it can describe a large number of physical phenomena, such as shallow water waves and ion waves. It is an important model for long-wave unidirectional propagation in weakly nonlinear dispersive media, but its numerical investigations are rarely made. For the initial-boundary value problem of the generalized BBM-KdV equations with homogeneous boundary conditions, a two-level nonlinear finite difference scheme with the second-order theoretical accuracy is proposed, which reasonably simulates the two conserved quantities of the problem. With a priori estimation, the existence and uniqueness of the difference solutions are dicussed. By the discrete functional analysis method the convergence and unconditional stability of the scheme are also proved. Finally, some numerical experiments verify the robustness of the proposed scheme.