A Finite Difference Method For The Variable-coefficient Nonlinear Schr(

In this text,we present a difference scheme for a class of non-linear Schrodinger equation with five variables.The topic will be divided into four parts for discussion:First chapter is the introduction part,introduces the development history and present situation of Schrodinger equation,and some research achievements in differ-ent fields.We also briefly explained the main work of this paper.In the second chapter,we discuss the initial-boundary value problem of the non-linear Schrodinger equation with variable coefficients of the five order.First,it is proved that the initial-boundary value problem satisfies two conservation properties.Secondly,the priori estimate for the solution of the initial-boundary value problem is obtained.The third chapter and the fourth chapter constructed the non-linear Schrodinger equation with variable coefficients is five times of the two layer and three layer difference format.And study the two kinds of formats to meet two and the difference of conservation properties the priori estimates.Finally,we discuss the stability and convergence of the difference scheme and the error estimation of solutions is presented.