Work

High-Order Numerical Approximation for 2D Time-Fractional Advection–Diffusion Equation under Caputo Derivative

Year: 2024

Type: article

Abstract: In this paper, we propose a novel approach for solving two-dimensional time-fractional advection–diffusion equations, where the fractional derivative is described in the Caputo sense. The discrete scheme is constructed based on the barycentric rational interpolation collocation method and the Gauss–Legendre quadrature rule. We employ the barycentric rational interpolation collocation method to approximate the unknown function involved in the equation. Through theoretical analysis, we establish the convergence rate of the discrete scheme and show its remarkable accuracy. In addition, we give some numerical examples, to illustrate the proposed method. All the numerical results show the flexible application ability and reliability of the present method.

Source: Fractal and Fractional

DOI: 10.3390/fractalfract8080474

Authors: Xindong Zhang, Yan Chen, Leilei Wei

Institutions: Guizhou University of Finance and Economics, Xinjiang Normal University, Henan 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: $3,069

Funders: Guizhou University of Finance and Economics, Natural Science Foundation of Xinjiang