Error Analysis and Numerical Simulations of Strang Splitting Method for Space Fractional Nonlinear Schrodinger Equation
Error Analysis and Numerical Simulations of Strang Splitting 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斯特分裂法误差分析与数值模拟
DOI：
10.1007/s10915-019-01050-w
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发表时间：
2019
影响因子：
2.5
通讯作者：
Zhao Xuan
中科院分区：
文献类型：
--
作者：
Zhai Shuying;Wang Dongling;Weng Zhifeng;Zhao Xuan
本文研究了一维、二维和三维空间分数阶非线性薛定谔方程周期边界条件的快速显式算子分裂方法.该方程分为线性和非线性部分：线性部分由傅立叶谱方法求解，该方法基于精确解，因此对时间步长没有稳定性限制;然后，由于可获得封闭形式的解，非线性子方程可解析求解。对离散质量守恒原理进行了严格的分析，并证明了算法的收敛速度。理论结果表明，该方法是无条件稳定的，时间上具有二阶精度，而空间精度依赖于解的正则性。一维、二维和三维的数值实验表明了该方法的有效性。
In this paper, we study a fast explicit operator splitting method for space fractional nonlinear Schrödinger equation in one (1D), two (2D) and three dimensions (3D) with periodic boundary conditions. The equation is split into linear and nonlinear parts: the linear part is solved by the Fourier spectral method, which is based on the exact solution and thus has no stability restriction on the time-step size; the nonlinear subequation is then solved analytically due to the availability of a closed-form solution. The rigorous analysis of the discrete mass conservation principle and the convergence rate of the proposed algorithm are proved. The theoretical results show the proposed method isunconditionally stable, second order accurate in time, whereas the spatial accuracy depends on the regularity of the solution. Numerical experiments for 1D, 2D and 3D cases demonstrate the efficiency of the proposed method.