A Conservative Finite Difference Research For Generalizd BBM-KdV Equation

In the study of nonlinear diffusion waves,the BBM–KdV equation occupies an important position 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,and its numerical studies are rarely involved.This paper studies the initial-boundary value problem of a class of generalized BBM-KdV equations with homogeneous boundary conditions.Two two-layer nonlinear finite difference schemes with secondorder theoretical accuracy and a third-order theoretical accuracy with second-order theoretical accuracy are respectively proposed.all that reasonably simulate one or two conserved quantities of the problem itself.For each difference scheme,the existence,uniqueness and a priori estimation of the difference decomposition are given,and the discrete functional analysis method is used to prove the second-order convergence and unconditional stability of the scheme.Finally,the numerical simulation experiment verifies that the numerical method we proposed is reliable.