拟线性薛定谔方程的 Strang 分裂法：收敛性、不稳定性与动力学
数值分析
2014-09-22 v5
摘要
我们研究了拟线性薛定谔方程的 Strang 分裂格式。我们建立了该格式对小初值解的收敛性。我们分析了数值格式的线性不稳定性，这解释了大初值解的数值爆破现象，并将其与拟线性薛定谔方程解的正则性解析破缺联系起来。针对超流薄膜方程的修正版本进行了数值测试。
引用
@article{arxiv.1305.7205,
title = {Strang Splitting Methods for a quasilinear Schr\"odinger equation - Convergence, Instability and Dynamics},
author = {Jianfeng Lu and Jeremy L. Marzuola},
journal= {arXiv preprint arXiv:1305.7205},
year = {2014}
}
备注
25 pages, 7 figures, References Updated, Figures added, Computations Extended and Material Re-organized, Additional Comments from Anonymous Referees incorporated, corrected convergence proof to address a loss of regularity due to a comment from L. Gauckler