@article{Li2023, 
author = {Xiao-Yu Li and Yu-Lan Wang and Zhi-Yuan Li},
title = {Numerical simulation for the fractional-in-space Ginzburg-Landau equation using Fourier spectral method},
year = {2023},
journal = {AIMS Mathematics},
volume = {8},
number = {1},
pages = {2407-2418},
keywords = {fractional Ginzburg-Landau equation, Laplacian operator, Fourier spectral method, numerical simulation},
url = {https://www.sciopen.com/article/10.3934/math.2023124},
doi = {10.3934/math.2023124},
abstract = {This paper uses the Fourier spectral method to study the propagation and interaction behavior of the fractional-in-space Ginzburg-Landau equation in different parameters and different fractional derivatives. Comparisons are made between the numerical and the exact solution, and it is found that the Fourier spectral method is a satisfactory and efficient algorithm for capturing the propagation of the fractional-in-space Ginzburg-Landau equation. Experimental findings indicate that the proposed method is easy to implement, effective and convenient in the long-time simulation for solving the proposed model. The influence of the fractional Laplacian operator on the fractional-in-space Ginzburg-Landau equation and some of the propagation behaviors of the 3D fractional-in-space Ginzburg-Landau equation are observed. In Experiment 2, we observe the propagation behaviors of the 3D fractional-in-space Ginzburg-Landau equation which are unlike any that have been previously obtained in numerical studies.}
}