Riesz空间分数阶非线性薛定谔方程的一种高效解法  

An Efficient Method for the Riesz Space Fractional Nonlinear Schrodinger Equation

作　　者：唐娇 王晚生 TANG Jiao;WANG Wansheng(College of Mathematics and Statistics, Changsha University of Science and Technology, Changsha 410114, China)

机构地区：[1]长沙理工大学数学与统计学院,湖南长沙410114

出　　处：《湖南理工学院学报（自然科学版）》2019年第1期13-19,共7页Journal of Hunan Institute of Science and Technology(Natural Sciences)

基　　金：国家自然科学基金项目(11771060;11371074)

摘　　要：现实生活中的很多物理现象只有将分数阶微积分同量子力学结合起来才能得到准确的表述,因此对薛定谔方程的研究也从整数阶扩充到了分数阶.本文利用时间分裂谱方法离散求解半经典体系中的Riesz空间分数阶非线性薛定谔方程.对该数值方法进行了稳定性分析和色散分析,并将不同网格下求得的数值解进行了对比.结果表明时间分裂谱方法具有高精度近似和无条件稳定性.Many physical phenomena in real life can only be accurately expressed by combining fractional calculus with quantum mechanics. Therefore, the study of Schrodinger equation is extended from integer order to fractional order. In this paper, time splitting spectral method was used to solve the Riesz space fractional nonlinear Schrodinger equation in the semiclassical regime. The stability analysis and dispersion analysis of the numerical method were carried out, and the numerical solutions obtained under different grids were compared for comparison. The results showed that the time-split spectrum method has high-precision approximation and unconditional stability.

关 键 词：Riesz空间分数阶薛定谔方程 傅里叶积分算子 时间分裂傅里叶谱方法 Riesz分数阶 色散分析 

分 类 号：O241.8[理学—计算数学]