Energy preserving relaxation method for space-fractional nonlinear Schrodinger equation
Energy preserving relaxation method for space-fractional nonlinear Schrodinger equation
复制标题
空间分数阶非线性薛定谔方程的保能松弛法
DOI：
10.1016/j.apnum.2019.11.008
复制
发表时间：
2020
影响因子：
2.8
通讯作者：
Yang Wei
中科院分区：
文献类型：
--
作者：
Cheng Bianru;Wang Dongling;Yang Wei
本文发展并分析了一类具有周期边界条件的空间分数阶非线性薛定谔方程(F-NLS)的能量守恒松弛格式。对于具有一般功率非线性的F-NLS，该方案可以保持离散的质量和能量。对于三次非线性F-NLS，严格地证明了数值方法在时间方向上的二阶收敛。给出了基于空间傅里叶谱近似的一维和二维情况的数值模拟，验证了该方法的理论分析。
In this paper, we develop and analyze an energy preserving relaxation scheme for a class of space fractional nonlinear Schrödinger equations (F-NLS) with periodic boundary condition. This scheme can preserve the discrete mass and energy for F-NLS with general power nonlinearity. The second order convergence in time direction for the numerical method is rigorously proved for the cubic nonlinear F-NLS. Some numerical simulations for 1D and 2D cases based on the Fourier spectral approximation in space are presented to validate the theoretical analysis of the proposed method.