|
| 摘要: |
| 本文将两个分裂龙格-库塔格式和分裂谱格式应用于半经典的Schr¨odinger 方
程。本文给出了格式的稳定性研究，并给出了当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。本文给出了
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可
靠的。 |
| 关键词: 非线性Schr¨odinger方程 分裂龙格-库塔格式 分裂谱格式 差分 |
| DOI： |
| 分类号:65M06; 65M30 |
| 基金项目: |
|
| Split-Step Methods for the Nonlinear Schr¨odinger equations and their applications in semiclassical case |
|
Xu Qiubin
|
| Abstract: |
| In this paper, two split step Runge-Kutta methods and a split step spectral method
for the nonlinear Schr¨odinger 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 are conditionally 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. |
| Key words: Nonlinear Schr¨odinger equation(NLS) split step Runge-Kutta method Split step spectral method difference scheme |
