Finite Difference Method For Nonlinear Schr (?) Dinger Equation With Positive Quintic Term

In this paper, we will discuss initial-boundary value problem of nonlinear Schr(?) dinger equation with the positive quintic terms, we give the conservation of finite difference scheme about initial-boundary value problem, the article will be divided into four parts, the first part is the introduction, introduces the development history and research status of the equation and applied to the lemma, we also simply introduced the main work of this article. The second part, we are analyzed the initial-boundary value problem of the equation. Firstly, we are discussed the existence of global solution, the following proved the initial-boundary value problem have the nature of mass conservation and energy conservation, finally we made a priori estimate for the solution of initial-boundary value problem. The third part, we are given the conservation difference scheme of the initial-boundary value problem of nonlinear Schr(?)dinger equation with the positive quintic terms, we are proved the existence of difference scheme solution and uniqueness, we are proved the conservation of difference scheme and made a priori estimate of the difference solution also. The fourth part, we are proved the Stability and convergence of difference scheme and given the error estimate.