含阻尼效应的非线性薛定谔方程的共形分裂高阶紧致差分格式  

The Conformal Splitting High-Order Compact Difference Scheme for Damped Nonlinear Schrödinger Equation

作　　者：罗奕杨 王兰 万隆 孔令华 LUO Yiyang;WANG Lan;WAN Long;KONG Linghua(School of Mathematics and Statistics,Jiangxi Normal University,Nanchang Jiangxi 330022,China;School of Primary Education,Yuzhang Normal University,Nanchang Jiangxi 330103,China)

机构地区：[1]江西师范大学数学与统计学院,江西南昌330022 [2]豫章师范学院小学教育学院,江西南昌330103

出　　处：《江西师范大学学报（自然科学版）》2022年第2期210-214,共5页Journal of Jiangxi Normal University(Natural Science Edition)

基　　金：国家自然科学基金(11961036);江西师范大学研究生创新基金(YJS2021068)的资助项目.

摘　　要：该文对含有阻尼效应的非线性薛定谔方程提出了一个新的共形分裂高阶紧致差分格式.首先利用分裂技巧,将复杂方程分裂为3个子问题;然后对于其中的非线性子问题,利用其逐点质量守恒的性质可以精确求解,避免了迭代,提高了计算效率;再利用了高阶紧致方法对空间进行离散,在基本不提高成本的情况下,提升了空间精度;最后通过理论分析与数值实验证明了该格式的高精度、稳定性以及保持共形质量守恒律.The new conformal splitting high-order compact difference scheme for damped nonlinear Schrödinger equation is proposed in this paper.Firstly,the complex equation is divided into three subproblems by using the splitting technique.Then,the nonlinear subproblem can be solved precisely by using the property of point-by-point mass conservation,which avoids iteration and improves computational efficiency.In addition,the high-order compact method is applied to discretize the space,which improves the spatial accuracy without increasing the cost.Finally,the high accuracy,stability and two conformal conservation laws of the scheme are proved by theoretical analysis and numerical experiments.

关 键 词：含阻尼效应的非线性薛定谔方程 分裂方法 高阶紧致格式 共形守恒律 

分 类 号：O241.8[理学—计算数学]