Mass- and Energy-Conserved Numerical Schemes for Nonlinear Schr ¨odinger Equations
Mass- and Energy-Conserved Numerical Schemes for Nonlinear Schr ¨odinger Equations
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DOI：
10.4208/cicp.2019.js60.05
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发表时间：
2019-02
影响因子：
3.7
通讯作者：
Xiaobing H. Feng;Hailiang Liu;Shufang Ma
中科院分区：
文献类型：
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作者：
Xiaobing H. Feng;Hailiang Liu;Shufang Ma
在本文中，我们提出了一族时间推进格式来逼近一般的非线性薛定谔方程。所提出的方案都满足质量守恒和能量守恒。截断和分散误差分析提供了每个建议的计划。高效的不动点迭代求解器也被构造来解决由此产生的非线性离散问题。作为一个副产品，一个有效的一步实现的BDF计划，以及获得。大量的数值实验证明了所提出的格式的收敛性和捕捉爆破现象的能力。
In this paper, we propose a family of time-stepping schemes for approximating general nonlinear Schrodinger equations. The proposed schemes all satisfy both mass conservation and energy conservation. Truncation and dispersion error analyses are provided for each proposed scheme. Efficient fixed-point iterative solvers are also constructed to solve the resulting nonlinear discrete problems. As a byproduct, an efficient one-step implementation of the BDF schemes is obtained as well. Extensive numerical experiments are presented to demonstrate the convergence and the capability of capturing the blow-up phenomenon of the proposed schemes.