Numerical Simulation Based on Interpolation Technique for Multi-Term Time-Fractional Convection–Diffusion Equations
This paper introduces a novel approach for solving multi-term time-fractional convection–diffusion equations with the fractional derivatives in the Caputo sense. The proposed highly accurate numerical algorithm is based on the barycentric rational interpolation collocation method (BRICM) in conjunct...
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| Format: | Article |
| Language: | English |
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MDPI AG
2024-11-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/8/12/687 |
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| _version_ | 1846104554072965120 |
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| author | Xindong Zhang Yan Chen Leilei Wei Sunil Kumar |
| author_facet | Xindong Zhang Yan Chen Leilei Wei Sunil Kumar |
| author_sort | Xindong Zhang |
| collection | DOAJ |
| description | This paper introduces a novel approach for solving multi-term time-fractional convection–diffusion equations with the fractional derivatives in the Caputo sense. The proposed highly accurate numerical algorithm is based on the barycentric rational interpolation collocation method (BRICM) in conjunction with the Gauss–Legendre quadrature rule. The discrete scheme constructed in this paper can achieve high computational accuracy with very few interval partitioning points. To verify the effectiveness of the present discrete scheme, some numerical examples are presented and are compared with the other existing method. Numerical results demonstrate the effectiveness of the method and the correctness of the theoretical analysis. |
| format | Article |
| id | doaj-art-399c600d583147709f7e1f5e0caa982b |
| institution | Kabale University |
| issn | 2504-3110 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj-art-399c600d583147709f7e1f5e0caa982b2024-12-27T14:27:00ZengMDPI AGFractal and Fractional2504-31102024-11-0181268710.3390/fractalfract8120687Numerical Simulation Based on Interpolation Technique for Multi-Term Time-Fractional Convection–Diffusion EquationsXindong Zhang0Yan Chen1Leilei Wei2Sunil Kumar3College of Big Data Statistics, Guizhou University of Finance and Economics, Guiyang 550025, ChinaCollege of General Studies, Xinjiang University of Technology, Hotan 848000, ChinaSchool of Mathematics and Statistics, Henan University of Technology, Zhengzhou 450001, ChinaDepartment of Mathematics, National Institute of Technology, Jamshedpur 831014, Jharkhand, IndiaThis paper introduces a novel approach for solving multi-term time-fractional convection–diffusion equations with the fractional derivatives in the Caputo sense. The proposed highly accurate numerical algorithm is based on the barycentric rational interpolation collocation method (BRICM) in conjunction with the Gauss–Legendre quadrature rule. The discrete scheme constructed in this paper can achieve high computational accuracy with very few interval partitioning points. To verify the effectiveness of the present discrete scheme, some numerical examples are presented and are compared with the other existing method. Numerical results demonstrate the effectiveness of the method and the correctness of the theoretical analysis.https://www.mdpi.com/2504-3110/8/12/687Caputo derivativebarycentric rational interpolationmulti-term time-fractional convection–diffusion equationGauss–Legendre quadrature rule |
| spellingShingle | Xindong Zhang Yan Chen Leilei Wei Sunil Kumar Numerical Simulation Based on Interpolation Technique for Multi-Term Time-Fractional Convection–Diffusion Equations Fractal and Fractional Caputo derivative barycentric rational interpolation multi-term time-fractional convection–diffusion equation Gauss–Legendre quadrature rule |
| title | Numerical Simulation Based on Interpolation Technique for Multi-Term Time-Fractional Convection–Diffusion Equations |
| title_full | Numerical Simulation Based on Interpolation Technique for Multi-Term Time-Fractional Convection–Diffusion Equations |
| title_fullStr | Numerical Simulation Based on Interpolation Technique for Multi-Term Time-Fractional Convection–Diffusion Equations |
| title_full_unstemmed | Numerical Simulation Based on Interpolation Technique for Multi-Term Time-Fractional Convection–Diffusion Equations |
| title_short | Numerical Simulation Based on Interpolation Technique for Multi-Term Time-Fractional Convection–Diffusion Equations |
| title_sort | numerical simulation based on interpolation technique for multi term time fractional convection diffusion equations |
| topic | Caputo derivative barycentric rational interpolation multi-term time-fractional convection–diffusion equation Gauss–Legendre quadrature rule |
| url | https://www.mdpi.com/2504-3110/8/12/687 |
| work_keys_str_mv | AT xindongzhang numericalsimulationbasedoninterpolationtechniqueformultitermtimefractionalconvectiondiffusionequations AT yanchen numericalsimulationbasedoninterpolationtechniqueformultitermtimefractionalconvectiondiffusionequations AT leileiwei numericalsimulationbasedoninterpolationtechniqueformultitermtimefractionalconvectiondiffusionequations AT sunilkumar numericalsimulationbasedoninterpolationtechniqueformultitermtimefractionalconvectiondiffusionequations |