分数阶非线性Schrodinger方程的守恒算法  

A Conservative Method for the Fractional Nonlinear Schrodinger 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）》2021年第5期465-471,共7页Journal of Jimei University：Natural Science

基　　金：福建省教育厅项目(JT180262,JAT190326);集美大学李尚大基金项目(ZC2018008);集美大学国家基金培育计划项目(ZP2020062,ZP2020054);福建省自然科学基金项目(2020J01703)。

摘　　要：利用傅里叶谱方法对空间分数阶非线性Schrodinger方程进行数值求解,并证明该格式保持了能量和质量的守恒性且无条件稳定。该方法在空间方向具有谱精度,在时间方向具有二阶精度。还对该格式进行误差分析及收敛性分析。最后通过数值实验验证了该算法的守恒性、准确性和有效性。In this paper,a Fourier spectral method for solving the fractional nonlinear Schrodinger equation with space fractional derivative was proposed.It was proved that the scheme conserved the mass and energy and was unconditionally stable.This method was of spectral accuracy in space and of second-order accuracy in time.Moreover,the error estimate and convergence of the scheme were also analyzed.Finally,numerical examples were presented to illustrate the conservation,accuracy and validity of the method.

关 键 词：分数阶非线性Schrodinger方程 谱方法 守恒律 收敛性 数值实验 

分 类 号：O175[理学—数学]