分数阶非线性Schr?dinger方程的时间分裂算法  

Time-splitting Method for the Fractional Nonlinear Schr?dinger Equation

作　　者：靳珊[1] 梁宗旗[1] JIN Shan;LIANG Zongqi(School of Science, Jimei University, Xiamen 361021,China)

机构地区：[1]集美大学理学院,福建厦门361021

出　　处：《集美大学学报（自然科学版）》2018年第1期63-69,共7页Journal of Jimei University：Natural Science

基　　金：福建省科技计划重点项目(2014H0034,2017H6015);福建省自然科学基金项目(2017J01557,2016J01310,2016J01309);集美大学李尚大基金项目(ZC2016022);福建省教育厅基金项目(JAT160247)

摘　　要：主要研究分数阶非线性Schr?dinger方程的时间分裂算法,将分数阶非线性Schr?dinger方程分裂成一个线性方程和一个非线性方程分别求解。其中,非线性方程可精确求解,并满足"点点守恒",而线性方程利用Crank-Nicolson差分格式离散求解。证明了该算法在离散形式下保持了原方程的质量和能量的守恒性,是无条件稳定的,收敛误差为O(h^2+τ~2)。最后通过数值实验验证了该算法的可行性和精度,说明该算法是一种简单有效的算法。A time-splitting method for solving the fractional nonlinear Schrodinger equation with space fractional derivative was proposed.In this method,the fractional nonlinear Schrodinger equation was split into a linear equation and a nonlinear equation,where the nonlinear equation could be solved exactly and satisfy4conservation of point7,and the linear equation could be solved by using Crank-Nicolson discretization method.The conservation of mass and energy for the original equation was kept in this method.The unconditional stability and the convergence with the truncation error0(h2+r2)were proved.Finally,numerical examples were presented to show that the method was both effective and accurate,which indicated that the method was simple and effective.

关 键 词：分数阶非线性Schradmger方程 分裂算法 守恒律 收敛性 数值实验 

分 类 号：O175[理学—数学]