Study On Spatial Extrapolation Of Finite Difference Equation For BBM-Burgers Equation

The propagation of wavelet in medium is affected not only by nonlinear diffusion but also by many complex dissipation principles,the Benjamnin Bona-Mahony add viscous term equation-u_xx,named BBM–Burgers equation,it contains a nonlinear diffusion and the influence of the dissipative term,so which has been as a kind of long wave propagation model to study,and study its numerical solution is also meaningful,however,most of the existing numerical methods can only achieve the second-order theoretical accuracy in the time layer and the space layer.In this paper,the initial boundary value problem of BBM-Bugers equation with homogeneous boundary conditions was numerically studied using Richardon's extrapolation theory,and a two-layer nonlinear Crank-Nicolson difference scheme with second-order theoretical precision in time layer and fourth-order theoretical precision in space layer was proposed.This scheme reasonably simulates a conservation property of the original problem,discusses the existence and uniqueness of difference decomposition,and analyzes the convergence and stability of the scheme by using the energy method.Numerical experiments show that the method is reliable.