非线性Schrödinger方程的算子分裂配点格式  

Operator Splitting Collocation Scheme for Nonlinear Schrödinger Equation

作　　者：姚梦丽 田朝薇[1] 翁智峰 YAO Mengli;TIAN Zhaowei;WENG Zhifeng(School of Mathematical Science,Huaqiao University,Quanzhou 362021,China)

机构地区：[1]华侨大学数学科学学院,福建泉州362021

出　　处：《华侨大学学报（自然科学版）》2023年第5期645-653,共9页Journal of Huaqiao University(Natural Science)

基　　金：国家自然科学基金资助项目(11701197);福建省自然科学基金面上资助项目(2022J01308);中央高校基本科研业务费专项基金资助项目(ZQN702)。

摘　　要：采用算子分裂格式结合重心Lagrange插值配点法求解非线性Schrödinger方程.首先,将非线性Schrödinger方程分解为线性部分和非线性部分,线性部分在空间方向上采用重心Lagrange插值配点格式进行离散,在时间方向上采用Crank-Nicolson格式进行离散,非线性部分采用解析求解;然后,对线性子问题空间半离散技术进行相容性分析.最后,采用数值算例进行验证.结果表明:算子分裂配点格式具有高精度,且满足离散的质量守恒和能量守恒.The operator splitting scheme combined with the barycentric Lagrange interpolation collocation method is used to solve the nonlinear Schrödinger equation.Firstly,the nonlinear Schrödinger equation is decomposed into linear and nonlinear parts.The linear part is discretized by the barycentric Lagrange interpolation collocation scheme in the spatial direction,and the Crank-Nicolson scheme is used for discretization in the time direction,the nonlinear part is solved analytically.Then,the consistency analysis of space semi discrete technique for linear subquestion is proved.Finally,numerical experiments are used for verification.The results show that the operator splitting collocation scheme has high accuracy and satisfies discrete conservation of mass and conservation of energy.

关 键 词：非线性Schrödinger方程 算子分裂格式 重心Lagrange插值配点法 CRANK-NICOLSON格式 

分 类 号：O241.82[理学—计算数学]