Analysis of a fully discrete scheme based on the barycentric interpolation method for nonlinear fractional reaction-convection-diffusion equations

Lingna Lu; Leilei Wei; Lingna Lu; Leilei Wei

doi:10.3934/nhm.2026058

Networks and Heterogeneous Media

2026, Volume 21, Issue 4: 1524-1543. doi: 10.3934/nhm.2026058

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Analysis of a fully discrete scheme based on the barycentric interpolation method for nonlinear fractional reaction-convection-diffusion equations

Lingna Lu ^{1
,
,},
Leilei Wei ²

1.
School of Basic Sciences, Zhengzhou University of Technology, Zhengzhou 450044, China
2.
School of Mathematics and Information Science, North Minzu University, Yinchuan 750021, China

Received: 04 March 2026 Revised: 28 June 2026 Accepted: 14 July 2026 Published: 17 July 2026

The primary objective of this study is to develop and analyze a numerical scheme to solve nonlinear fractional reaction-convection-diffusion equations, where the fractional derivative is interpreted in the Caputo sense. First, the nonlinear system is linearized using a direct linearization strategy, after which a barycentric rational interpolation method is employed to construct a fully discrete numerical scheme. A rigorous theoretical framework is established to demonstrate the stability and convergence of the proposed method. To corroborate the theoretical findings, several numerical experiments are conducted, illustrating the method's accuracy, robustness, and computational efficiency. This work advances the numerical analysis of nonlinear systems characterized by fractional-order dynamics and provides effective computational tools to model complex processes in various scientific and engineering contexts.
- Caputo derivative,
- barycentric rational interpolation,
- reaction-convection-diffusion equation
Citation: Lingna Lu, Leilei Wei. Analysis of a fully discrete scheme based on the barycentric interpolation method for nonlinear fractional reaction-convection-diffusion equations[J]. Networks and Heterogeneous Media, 2026, 21(4): 1524-1543. doi: 10.3934/nhm.2026058

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Abstract

The primary objective of this study is to develop and analyze a numerical scheme to solve nonlinear fractional reaction-convection-diffusion equations, where the fractional derivative is interpreted in the Caputo sense. First, the nonlinear system is linearized using a direct linearization strategy, after which a barycentric rational interpolation method is employed to construct a fully discrete numerical scheme. A rigorous theoretical framework is established to demonstrate the stability and convergence of the proposed method. To corroborate the theoretical findings, several numerical experiments are conducted, illustrating the method's accuracy, robustness, and computational efficiency. This work advances the numerical analysis of nonlinear systems characterized by fractional-order dynamics and provides effective computational tools to model complex processes in various scientific and engineering contexts.

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