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<p>In this paper, we propose a novel approach for solving the 2D time-space fractional convection-diffusion equation (2DTSFCDE), where the fractional derivative is described as the Caputo sense in time and Caputo–Fabrizio sense in space. We construct an efficient linear discrete format using barycentric rational interpolation collocation method (BRICM) and Gauss–Legendre quadrature rule. We utilize the BRICM technique to estimate the function that is not known within the equation. Through theoretical analysis, we give error estimates for both the exact and numerical solutions, and the efficacy of the suggested approach is validated through two numerical examples.</p>

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High precision interpolation method for mixed 2D time-space fractional convection-diffusion equation

  • 期刊论文

  • 发表日期：

    2025年9月9日

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  • Yan Chen,
  • Xindong Zhang,
  • Leilei Wei

摘要

In this paper, we propose a novel approach for solving the 2D time-space fractional convection-diffusion equation (2DTSFCDE), where the fractional derivative is described as the Caputo sense in time and Caputo–Fabrizio sense in space. We construct an efficient linear discrete format using barycentric rational interpolation collocation method (BRICM) and Gauss–Legendre quadrature rule. We utilize the BRICM technique to estimate the function that is not known within the equation. Through theoretical analysis, we give error estimates for both the exact and numerical solutions, and the efficacy of the suggested approach is validated through two numerical examples.