@article{Zhu2026, 
author = {Hui Zhu and Lei Yang and Ruimin Zhang and Yuntao Jia},
title = {A coupled numerical method for time-fractional convection-diffusion equations based on compressed Legendre polynomials},
year = {2026},
journal = {AIMS Mathematics},
volume = {11},
number = {7},
pages = {19488-19515},
keywords = {coupled numerical method, compressed Legendre polynomials, semi-discrete scheme, time fractional convection-diffusion equations},
url = {https://www.sciopen.com/article/10.3934/math.2026792},
doi = {10.3934/math.2026792},
abstract = {In this paper, we develop a novel coupled numerical method for time-fractional convection-diffusion equations. First, in the temporal dimension, a derivative-based linear interpolation is utilized to approximate the time partial derivative. Then, we construct a high-order approximate scheme for the temporal fractional derivative, which transforms the original partial differential equation into a semi-discrete ordinary differential system involving only spatial variables. In the spatial dimension, a standard orthogonal basis is constructed by using compressed Legendre polynomials. Combining the concept of    ε-approximate solutions, we derive the numerical solution of the semi-discrete scheme. Convergence analysis and numerical experiments demonstrate that the proposed algorithm achieves second-order convergence in time, and the spatial convergence accuracy improves as the Legendre polynomial degree and compression level increase.}
}