非线性Schrdinger方程的高精度守恒差分格式  

A HIGH ACCURATE AND CONSERVATIVE FINITE DIFFERENCE SCHEME FOR NONLINEAR SCHRDINGER EQUATION

作　　者：张鲁明[1] 

机构地区：[1]南京航空航天大学数学系,南京210016

出　　处：《应用数学学报》2005年第1期178-186,共9页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(10471023)资助项目.

摘　　要：本文首先分析线性Schrodinger方程一种高阶差分格式的构造方法,得到方程的耗散项.在此基础上对三次非线性Schrodinger方程,提出了一种精度为O(r2+h2)的差分格式,证明了该格式保持了连续方程的两个守恒量,且是收敛的与稳定的.并通过数值例子与已有隐格式进行了比较,结果表明,本文格式在计算量类似的情况下,提高了数值精度.In this paper, we, at first, considered a sort of method constructed high accurate finite difference scheme for linear Schrodinger equation and get dissipation term of the equation. Next, we proposed a conservative finite difference scheme with precision O (r2 + h2) for the nonlinear Schrodinger equation. It is proved that the scheme preserves two conservative quantities and is convergent and stable. The numerical results show that the scheme has higher precision than the other implicit schemes.

关 键 词：非线性SCHROEDINGER方程 高阶差分格式 隐格式 耗散项 类似 守恒量 收敛 连续方程 精度 数值 

分 类 号：O175[理学—数学] O122.3[理学—基础数学]