非线性Schrödinger方程的龙格库塔配点格式  

Runge-Kutta Collocation Scheme for Nonlinear Schrödinger Equation

作　　者：姚梦丽 滕宇航 赖艺颖 翁智峰 YAO Mengli;TENG Yuhang;LAI Yiying;WENG Zhifeng(School of Mathematical Sciences,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）》2024年第4期534-542,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4阶龙格库塔方法结合重心Lagrange插值配点法求解非线性Schrödinger方程。首先,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4阶龙格库塔方法离散,从而得到非线性Schrödinger方程的龙格库塔配点格式。其次,对全离散格式进行相容性分析。结果表明:龙格库塔配点格式具有高精度,且满足离散的质量和能量守恒。The fourth order Runge-Kutta method and barycentric Lagrange interpolation collocation method are used to solve the nonlinear Schrödinger equation.Firstly,the barycentric Lagrange interpolation collocation scheme is discreted in the spatial direction,and the fourth-order Runge-Kutta method is discreted in the temporal direction.The Runge-Kutta collocation scheme of the nonlinear Schrödinger equation is obtained.Secondly,the consistency analysis of the fully discrete scheme is analyzed.The results show that the Runge-Kutta collocation scheme has the high accuracy and satisfies the conservation of discrete mass and energy.

关 键 词：非线性Schrödinger方程 4阶龙格库塔方法 重心Lagrange插值配点 相容性分析 

分 类 号：O241.82[理学—计算数学]