Research On Finite Difference Solutions For Symmetric Regularized Long-wave Equation

In this paper, the finite difference method for the homogenous initial boundary value problem of symmetric regularized long-wave equation is considered. The main idea of the finite difference method is as follows: We consider the discrete difference equation with the finite alphas as approximate substitution for the differential equation with the continuous variant and boundary conditions. And the numerical solutions of difference equation are regarded as the approximate solutions for the differential equation.Firstly , one energy conservative finite difference scheme for SRLW equation of two levels and two of three levels are proposed in this paper. The error estimates are proved in theory. And, on the basis of priori estimates, convergence and stability of the difference solutions are proved by discrete functional analysis method. Furthermore, two energy conservative finite difference schemes for generalized symmetric regularized long-wave equation are also considered. The energy conservation, error estimate, convergence and stability of the difference solution are proved in theory. At last, numerical results demonstrate that the method is efficient and reliable. And the schemes of three levels are superior.The difference method is also applicable for the periodic problem of SRLW equation, the initial-boundary problems of higher dimensional SRLW equation and SRLW equation with damping term.