TY  - JOUR
AU  - Li, Xiao-Yu
AU  - Wang, Yu-Lan
AU  - Li, Zhi-Yuan
PY  - 2023
TI  - Numerical simulation for the fractional-in-space Ginzburg-Landau equation using Fourier spectral method
JO  - AIMS Mathematics
SP  - 2407
EP  - 2418
VL  - 8
IS  - 1
AB  - 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.
UR  - https://doi.org/10.3934/math.2023124
DO  - 10.3934/math.2023124