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| 摘要: |
| 本文研究了半经典的Schrödinger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. |
| 关键词: 非线性Schrö dinger方程 分裂龙格-库塔格式 分裂谱格式 差分格式 |
| DOI： |
| 分类号:O241.82 |
| 基金项目:国家社会科学基金资助(21BTJ030). |
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| SPLIT-STEP METHODS FOR THE NONLINEAR SCHRÖDINGER EQUATIONS AND THEIR APPLICATIONS IN SEMICLASSICAL CASE |
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XU Qiu-bin
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| Abstract: |
| In this paper,two split step Runge-Kutta methods and a split step spectral method for the nonlinear Schrödinger 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 Schrö dinger equation(NLS) split step Runge-Kutta method Split step spectral method difference scheme |
