半经典Schrodinger方程的几个分裂数值格式  

SPLIT-STEP METHODS FOR THE NONLINEAR SCHRODINGER EQUATIONS AND THEIR APPLICATIONS IN SEMICLASSICAL CASE

作　　者：许秋滨[1] XU Qiu-bin(School of Mathematics,Nanjing Audit University,Nanjing 211815,China)

机构地区：[1]南京审计大学数学学院,江苏南京211815

出　　处：《数学杂志》2025年第2期161-172,共12页Journal of Mathematics

基　　金：国家社会科学基金资助(21BTJ030).

摘　　要：本文研究了半经典的Schrodinger方程的两个分裂龙格-库塔格式和分裂谱格式.给出了格式的稳定性,并研究了当β=0时的平面波解.通过线性化的分析方法可知两个龙格-库塔格式是条件稳定的,谱格式是绝对稳定的.最后给出了格式的截断误差并与文[1]中的格式进行了数值比较,结果表明本文的格式是有效的和可靠的.In this paper,two split step Runge-Kutta methods and a split step spectral method for the nonlinear Schrodinger equations and their application in the semiclassical regimes are studied.The conservative properties of the schemes are obtained and the plane wave solution with β=0 is analysised.The two Runge-Kutta schemes areconditionally stable by linearized analysis and the split step spectral method is unconditionally stable.The trunction error of the schemes are discuassed.Furthermore,the computing results are compared with the two time-splitting spectral methods which are constructed in[1].The numerical experiments demonstrate that our algorithms are effective and reliable.

关 键 词：非线性SCHRODINGER方程 分裂龙格-库塔格式 分裂谱格式 差分格式 

分 类 号：O241.82[理学—计算数学]