An energy conservative difference scheme for the nonlinear fractional Schrodinger equations
An energy conservative difference scheme for the nonlinear fractional Schrodinger equations
复制标题
非线性分数阶薛定谔方程的能量守恒差分格式
DOI：
10.1016/j.jcp.2014.03.037
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发表时间：
2015
影响因子：
4.1
通讯作者：
Huang Chengming
中科院分区：
文献类型：
--
作者：
Wang Pengde;Huang Chengming
本文研究了非线性Riesz空间分数阶Schrodinger方程的能量守恒Crank-Nicolson差分格式。我们给出了严格的守恒性质，包括质量守恒和能量守恒的离散意义上的分析。利用Brouwer不动点定理证明了差分解的存在性。利用能量法证明了差分解的唯一性，并在l2范数下，以时间步长τ和网格尺寸h收敛于O（τ 2+ h2）阶.最后给出了一个线性化的迭代算法，并通过数值实验验证了理论结果。
In this paper, an energy conservative Crank–Nicolson difference scheme for nonlinear Riesz space-fractional Schrödinger equations is studied. We give a rigorous analysis of the conservation properties, including mass conservation and energy conservation in the discrete sense. Based on Brouwer fixed point theorem, the existence of the difference solution is proved. By virtue of the energy method, the difference solution is shown to be unique and convergent at the order of O (τ 2+ h 2) in the l 2-norm with time step τ and mesh size h. Finally a linearized iterative algorithm is presented and numerical experiments are given to confirm the theoretical results.