Work

Convergence of a Structure-Preserving Scheme for the Space-Fractional Ginzburg–Landau–Schrödinger Equation

Year: 2026

Type: article

Abstract: We present a linearly implicit and structure-preserving scheme to solve the space-fractional Ginzburg–Landau–Schrödinger equation. The fully discrete scheme is obtained by combining the modified leap-frog method in the temporal direction and the finite difference methods in the spatial direction. It is shown that the scheme can be unconditionally energy-stable. In particular, the equation becomes the space-fractional Schrödinger equation. Then, the scheme can keep both the discrete mass and energy conserved. Moreover, convergence of the scheme is obtained. Numerical experiments are performed to confirm the theoretical results.

Source: Fractal and Fractional

DOI: 10.3390/fractalfract10010056

Authors: Hongyu Qin, Haoyue Jiang, Xiaoli Chen

Institutions: Wuhan Institute of Technology, Huazhong University of Science and Technology, China University of Geosciences, Shenzhen Research Institute of China University of Geosciences

Language: English

Topic: Numerical methods for differential equations

Subfield: Numerical Analysis

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $3,258

Funders: National Natural Science Foundation of China, Natural Science Foundation of Hubei Province, Natural Science Foundation of Chongqing