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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Main Authors: Xindong Zhang, Yan Chen, Leilei Wei, Sunil Kumar
Format: Article
Language:English
Published: MDPI AG 2024-11-01
Series:Fractal and Fractional
Subjects:
Online Access:https://www.mdpi.com/2504-3110/8/12/687
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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.
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institution Kabale University
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language English
publishDate 2024-11-01
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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
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AT leileiwei numericalsimulationbasedoninterpolationtechniqueformultitermtimefractionalconvectiondiffusionequations
AT sunilkumar numericalsimulationbasedoninterpolationtechniqueformultitermtimefractionalconvectiondiffusionequations