求解Schrdinger方程的高阶紧致差分格式  

High-Order Compact Difference Method for Solving the Schrdinger Equation

作　　者：热娜.阿斯哈尔 阿不都热西提.阿不都外力 

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：《新疆大学学报（自然科学版）》2012年第2期182-185,190,共5页Journal of Xinjiang University(Natural Science Edition)

基　　金：国家自然科学基金(10961024);新疆高校科研计划资助(XJEDU2007102)

摘　　要：基于Richardson外推法提出了一种求解Schrdinger方程的高阶紧致差分方法.该方法首先利用二阶微商的四阶精度紧致差分逼近公式对原方程进行求解,然后利用Richardson外推技术外推一次,得到了Schrdinger方程具有O(r^4+h^4)精度的数值解.通过Fourier分析方法证明了该格式是无条件稳定的.数值实验验证了该方法的高阶精度及有效性.A high-order compact difference method based on the Richardson extrapolation technique is proposed to solve the SchrSdinger equation. For a particular implementation, firstly, numerical results are obtained on the fourth-order compact difference formulas for the second derivatives. Then, the Richardson extrapolation method is used to get an accuracy solution for the SchrSdinger equation, which is fourth order in space and fourth order in time. It is proved to be unconditionally stable by Fourier analysis. Numerical experiments are made to demonstrate the high accuracy and validity of this method.

关 键 词：Schrdinger方程 高阶紧致格式 RICHARDSON外推法 高精度 

分 类 号：O241.82[理学—计算数学]