Numerical simulation for the fractional-in-space Ginzburg-Landau equation using Fourier spectral method

AIMS Mathematics

article

Xiao-Yu Li¹  Yu-Lan Wang¹  Zhi-Yuan Li¹ 

[1] Department of Mathematics, Inner Mongolia University of Technology;College of Date Science and Application, Inner Mongolia University of Technology

关键词: fractional Ginzburg-Landau equation;    Laplacian operator;    Fourier spectral method;    numerical simulation;   

DOI  :  10.3934/math.2023124

学科分类：地球科学(综合)

来源: AIMS Press

【 摘 要 】

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.

【 授权许可】

CC BY