Work

A High-Precision Numerical Method for the Fractional-in-Time Complex Ginzburg–Landau Equation with Periodic Boundary Condition

Year: 2025

Type: article

Abstract: This paper investigates the chaotic and pattern dynamics of the time-fractional Ginzburg–Landau equation. First, we propose a high-precision numerical method that combines finite difference schemes with an improved Grünwald–Letnikov fractional derivative approximation. Subsequently, the effectiveness of the proposed method is validated through systematic comparisons with classical numerical approaches. Finally, numerical simulations based on this method reveal rich dynamical phenomena in the fractional Ginzburg–Landau equation: the system exhibits complex behaviors including chaotic oscillations and novel two- and three-dimensional pattern structures. This study not only advances the theoretical development of numerical solutions for fractional GLE but also provides a reliable computational tool for deeper understanding of its complex dynamical mechanisms.

Source: Fractal and Fractional

DOI: 10.3390/fractalfract9110738

Authors: Wei Zhang, Yulan Wang

Institutions: Jining Normal University, Inner Mongolia University of Technology

Language: English

Topic: Fractional Differential Equations Solutions

Subfield: Modeling and Simulation

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $3,258

Funders: Inner Mongolia University, Natural Science Foundation of Inner Mongolia, Inner Mongolia University of Technology