Fourier spectral method with an adaptive time strategy for nonlinear fractional Schrodinger equation
Fourier spectral method with an adaptive time strategy for nonlinear fractional Schrodinger equation
复制标题
非线性分数阶薛定谔方程的自适应时间策略傅里叶谱方法
DOI：
10.1002/num.22453
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发表时间：
2020
影响因子：
3.9
通讯作者：
She Zihang
中科院分区：
文献类型：
--
作者：
Qu Haidong;She Zihang
针对分数阶非线性薛定谔(FNLS)方程的周期初值问题，提出了一种具有自适应时间步长的傅立叶谱方法。首先，我们证明了半离散傅里叶谱格式的质量守恒定律和能量守恒定律。其次，在相应的分数阶Soblev空间中给出了半离散格式的误差估计。然后，设计了一种自适应的时间步长策略来减少中央处理单元(CPU)的时间。最后，对一维FNLSS、二维FNLSS和三维FNLSS的数值实验表明，与固定时间步长相比，自适应策略可以将CPU时间减少近一半。
In this paper, a Fourier spectral method with an adaptive time step strategy is proposed to solve the fractional nonlinear Schrödinger (FNLS) equation with periodic initial value problem. First, we prove the conservation law of the mass and the energy for the semi‐discrete Fourier spectral scheme. Second, the error estimation of the semi‐discrete scheme is given in the relevant fractional Sobolev space. Then, an adaptive time‐step strategy is designed to reduce central processing unit (CPU) time. Finally, the numerical experiments for the one‐, two‐ and three‐dimensional FNLSs, show that the adaptive strategy, compared to the constant time step, can reduce the CPU‐time by almost half.