Barycentric rational interpolation method for solving time-dependent fractional convection-diffusion equation

Jin Li; Yongling Cheng; Jin Li; Yongling Cheng

doi:10.3934/era.2023205

Electronic Research Archive

2023, Volume 31, Issue 7: 4034-4056. doi: 10.3934/era.2023205

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Barycentric rational interpolation method for solving time-dependent fractional convection-diffusion equation

Jin Li ,
Yongling Cheng ^,

School of Science, Shandong Jianzhu University, Jinan 250101, China

Received: 26 March 2023 Revised: 07 May 2023 Accepted: 14 May 2023 Published: 24 May 2023

The time-dependent fractional convection-diffusion (TFCD) equation is solved by the barycentric rational interpolation method (BRIM). Since the fractional derivative is the nonlocal operator, we develop a spectral method to solve the TFCD equation to get the coefficient matrix as a full matrix. First, the fractional derivative of the TFCD equation is changed to a nonsingular integral from the singular kernel to a density function. Second, efficient quadrature of the new Gauss formula are constructed to simply compute it. Third, matrix equation of discrete the TFCD equation is obtained by the unknown function replaced by a barycentric rational interpolation basis function. Then, the convergence rate of BRIM is proved. Finally, a numerical example is given to illustrate our result.
- barycentric rational interpolation,
- collocation method,
- time-dependent fractional convection-diffusion equation,
- fractional derivative
Citation: Jin Li, Yongling Cheng. Barycentric rational interpolation method for solving time-dependent fractional convection-diffusion equation[J]. Electronic Research Archive, 2023, 31(7): 4034-4056. doi: 10.3934/era.2023205

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Abstract

The time-dependent fractional convection-diffusion (TFCD) equation is solved by the barycentric rational interpolation method (BRIM). Since the fractional derivative is the nonlocal operator, we develop a spectral method to solve the TFCD equation to get the coefficient matrix as a full matrix. First, the fractional derivative of the TFCD equation is changed to a nonsingular integral from the singular kernel to a density function. Second, efficient quadrature of the new Gauss formula are constructed to simply compute it. Third, matrix equation of discrete the TFCD equation is obtained by the unknown function replaced by a barycentric rational interpolation basis function. Then, the convergence rate of BRIM is proved. Finally, a numerical example is given to illustrate our result.

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