带五次项的非线性Schrodinger方程的守恒差分格式

A CONSERVATIVE FINITE DIFFERENCE SCHEME FOR NONLINEAR SCHRODINGER EQUATION INVOLVING QUINTIC TERMS

本文研究带有五次项的非线性Schrodinger方程初边值问题的有限差分法,其中方程中二阶偏导数项的系数、五次项的系数及初值满足下面的条件(1.6).针对此问题,我们研究了一个守恒差分格式,在条件(1.6)下,差分解的L^(∞)模先验估计被得到.在此基础上,我们得到了差分解最优L^(2)模的误差估计.

In this paper,we shall study the finite difference method for the approximate solution of the initial-boundary value problem for the nonlinear Schrodinger equation involving quintic terms.We assume that the coefficient of second order partial derivative term,the coefficient of quintic and initial value uo satisfies the following condition(1.6).Due to this problem,we study a conservative difference scheme,priori estimates of the finite difference solutions on L^(∞)norm are obtained,on this basis,error estimates of optimal order on L^(2)norm of the finite difference solutions are obtained.