2维薛定谔方程的一种高精度紧致差分格式  

The High-Order Compact Difference Scheme forTwo-Dimensional Schr dinger Equation

作　　者：依力米努尔·尼扎木 开依沙尔·热合曼[1] ELMINUR Nizam;KAYSA Rahman(College of Mathematics and System Science,Xinjiang University,Urumqi Xinjiang 830046,China)

机构地区：[1]新疆大学数学与系统科学学院,新疆乌鲁木齐830046

出　　处：《江西师范大学学报（自然科学版）》2024年第2期189-193,共5页Journal of Jiangxi Normal University(Natural Science Edition)

基　　金：国家自然科学基金(11461069);新疆大学博士启动基金(BS150204)资助项目.

摘　　要：该文对2维薛定谔方程利用局部一维化方法,将2维方程分裂为x、y方向的2个1维薛定谔方程,然后采用6阶紧致格式的离散方法来处理空间变量的2阶导数项,将薛定谔方程转化为一个常微分方程组.通过L-稳定Simpson方法对上述空间离散化得到的常微分方程进行离散化,得到了一种具有空间6阶精度和时间3阶精度的格式,并证明了该格式无条件稳定性.并通过数值模拟和对比方法验证了格式的有效性.In this paper,the two-dimensional Schr dinger equation is split into two one-dimensional Schr dinger equations in x and y direction by using the local one-dimensional method.Then,the sixth-order compact scheme is used to deal with the second derivative terms of spatial variables,and the Schr dinger equation is transformed into a system of ordinary differential equations.The L-stable Simpson method is used to discretize the ordinary differential equation obtained from the space discretization.Therefore,a scheme with spatial sixth-order accuracy and temporal third-order accuracy is obtained,and the unconditional stability of the scheme is proved.Finally,the validity of the scheme is verified by numerical simulation and comparison.

关 键 词：2维薛定谔方程 高精度紧致差分格式 局部1维化方法 L-稳定Simpson方法 

分 类 号：O241.82[理学—计算数学]