基于变限积分法的非线性Schr dinger方程的数值格式  

Numerical Scheme of Nonlinear Schr dinger Equation Based on Variable Limit Integral Method

作　　者：张燕 冯立新[1] ZHANG Yan;FENG Lixin(School of Mathematical Sciences,Heilongjiang University,Harbin 150080,China)

机构地区：[1]黑龙江大学数学科学学院,哈尔滨150080

出　　处：《吉林大学学报（理学版）》2023年第2期303-309,共7页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金面上项目(批准号:11871198);黑龙江省自然科学基金(批准号:LH2022A021).

摘　　要：首先,利用变限积分法和四阶Runge-Kutta法分别离散含五次项的非线性Schr dinger方程的空间和时间变量,并构造初边值问题的全离散格式;其次,在理论上证明其数值解的有界性、存在唯一性以及收敛阶;最后,用数值模拟验证理论分析的有效性.Firstly,the variable limit integral method and the fourth-order Runge-Kutta method were used to discretize the spatial and temporal variables of a nonlinear Schr dinger equation with a fifth order term,respectively,and a fully-discrete scheme for the initial boundary value problem was constructed.Secondly,we theoretically proved the boundedness,existence,uniqueness and the order of convergence of the numerical solution.Finally,the numerical simulations verified the validity of the theoretical analysis.

关 键 词：Schr dinger方程 变限积分法 四阶Runge-Kutta法 收敛性分析 

分 类 号：O241.82[理学—计算数学]