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Papers published in the English version of the journal

Local discontinuous Galerkin method for the variable-order fractional mobile-immobile advection-dispersion equation

Miaomiao Yang^a, Lijie Liu^b, Leilei Wei<sup>b

a</sup> General Education Center, Zhengzhou Business University, Zhengzhou, China
^b School of Mathematics and Statistics, Henan University of Technology, Zhengzhou, China

Abstract: In this paper, a high-order local discontinuous Galerkin (LDG) method is proposed to solve the variable-order (VO) fractional mobile-immobile advection-dispersion equation with the Coimbra VO fractional derivative operator. The LDG method in space and the finite difference method in time are the foundations for the method proposed in this paper. We demonstrate that the scheme is unconditionally stable and convergent for $\alpha(t)\in(0,1)$. Finally, the correctness of the theoretical analysis is verified by some numerical experiments.

Key words: the Coimbra VO fractional derivative, stability, error estimate.

Received: 10.03.2024
Revised: 17.10.2024
Accepted: 26.03.2025

Language: English

 English version: Computational Mathematics and Mathematical Physics, 2025, 65:2, 308–319