Barycentric rational interpolation method for solving time-dependent fractional convection-diffusion equation
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. Firs...
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| Format: | Article |
| Language: | English |
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AIMS Press
2023-05-01
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| Series: | Electronic Research Archive |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/era.2023205?viewType=HTML |
| _version_ | 1827823159737319424 |
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| author | Jin Li Yongling Cheng |
| author_facet | Jin Li Yongling Cheng |
| author_sort | Jin Li |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-12T02:07:13Z |
| format | Article |
| id | doaj.art-6a8b05c19a1f49ae93faa098ef8cabc9 |
| institution | Directory Open Access Journal |
| issn | 2688-1594 |
| language | English |
| last_indexed | 2024-03-12T02:07:13Z |
| publishDate | 2023-05-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Electronic Research Archive |
| spelling | doaj.art-6a8b05c19a1f49ae93faa098ef8cabc92023-09-07T02:15:54ZengAIMS PressElectronic Research Archive2688-15942023-05-013174034405610.3934/era.2023205Barycentric rational interpolation method for solving time-dependent fractional convection-diffusion equationJin Li0 Yongling Cheng1School of Science, Shandong Jianzhu University, Jinan 250101, ChinaSchool of Science, Shandong Jianzhu University, Jinan 250101, ChinaThe 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.https://www.aimspress.com/article/doi/10.3934/era.2023205?viewType=HTMLbarycentric rational interpolationcollocation methodtime-dependent fractional convection-diffusion equationfractional derivative |
| spellingShingle | Jin Li Yongling Cheng Barycentric rational interpolation method for solving time-dependent fractional convection-diffusion equation Electronic Research Archive barycentric rational interpolation collocation method time-dependent fractional convection-diffusion equation fractional derivative |
| title | Barycentric rational interpolation method for solving time-dependent fractional convection-diffusion equation |
| title_full | Barycentric rational interpolation method for solving time-dependent fractional convection-diffusion equation |
| title_fullStr | Barycentric rational interpolation method for solving time-dependent fractional convection-diffusion equation |
| title_full_unstemmed | Barycentric rational interpolation method for solving time-dependent fractional convection-diffusion equation |
| title_short | Barycentric rational interpolation method for solving time-dependent fractional convection-diffusion equation |
| title_sort | barycentric rational interpolation method for solving time dependent fractional convection diffusion equation |
| topic | barycentric rational interpolation collocation method time-dependent fractional convection-diffusion equation fractional derivative |
| url | https://www.aimspress.com/article/doi/10.3934/era.2023205?viewType=HTML |
| work_keys_str_mv | AT jinli barycentricrationalinterpolationmethodforsolvingtimedependentfractionalconvectiondiffusionequation AT yonglingcheng barycentricrationalinterpolationmethodforsolvingtimedependentfractionalconvectiondiffusionequation |