一类耦合非线性薛定谔方程的线性隐式差分格式  

A Linearly Implicit Conservative Scheme for a Coupled Nonlinear Schr¨odinger Equations

作　　者：李胜平 王俊杰 LI Shengping;WANG Junjie(School of Mathematics and Statistics,Pu’er University,Pu’er 665000)

机构地区：[1]普洱学院数学与统计学院,普洱665000

出　　处：《工程数学学报》2025年第2期311-328,共18页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金(12161070)。

摘　　要：薛定谔方程一类重要的数学物理方程,在工程领域具有重要的应用。基于高阶有限差分法、Crank-Nicolson方法和Leap-frog方法,对耦合非线性薛定谔方程的守恒差分格式进行了研究。所提出的数值格式是解耦的、线性的,并满足离散质量和能量守恒律。同时,也讨论了数值格式的存在性、唯一性、稳定性和收敛性,证明该格式的精度为O(τ^(2)+h^(4))。最后,给出了数值实验结果,验证了该格式的有效性。The Schrodinger equation is an important class of mathematical physics equations,and it has significant applications in engineering.The conservative difference scheme for the coupled nonlinear Schrodinger equation is studied based on the high-orderfinite difference method,the Crank-Nicolson,and the Leap-frog method.Moreover,the proposed numerical formulation is decoupled,linear,and it satisfies the discrete mass and energy conservation laws.The existence,uniqueness,stability and convergence of the numerical formulation are discussed,and it is shown that the numerical formulation is of the accuracy O(τ^(2)+h^(4)).The numerical experiments are given,and their results verify the efficiency of the scheme.

关 键 词：薛定谔方程 守恒格式 稳定性 收敛性 

分 类 号：O242.2[理学—计算数学]