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

Xiao-Yu Li; Yu-Lan Wang; Zhi-Yuan Li; Xiao-Yu Li; Yu-Lan Wang; Zhi-Yuan Li

doi:10.3934/math.2023124

AIMS Mathematics

2023, Volume 8, Issue 1: 2407-2418. doi: 10.3934/math.2023124

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Research article

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

1.
Department of Mathematics, Inner Mongolia University of Technology, Hohhot, 010051, China
2.
College of Date Science and Application, Inner Mongolia University of Technology, Hohhot, 010080, China

Received: 02 August 2022 Revised: 19 September 2022 Accepted: 26 September 2022 Published: 02 November 2022
MSC : 78M22, 81Q05

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.
- fractional Ginzburg-Landau equation,
- Laplacian operator,
- Fourier spectral method,
- numerical simulation
Citation: Xiao-Yu Li, Yu-Lan Wang, Zhi-Yuan Li. Numerical simulation for the fractional-in-space Ginzburg-Landau equation using Fourier spectral method[J]. AIMS Mathematics, 2023, 8(1): 2407-2418. doi: 10.3934/math.2023124

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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.

References

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