Numerical Solutions for Systems of Fractional and Classical Integro-Differential Equations via Finite Integration Method Based on Shifted Chebyshev Polynomials
In this paper, the finite integration method and the operational matrix of fractional integration are implemented based on the shifted Chebyshev polynomial. They are utilized to devise two numerical procedures for solving the systems of fractional and classical integro-differential equations. The fr...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-08-01
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| Series: | Fractal and Fractional |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2504-3110/5/3/103 |
| _version_ | 1797519179048288256 |
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| author | Ampol Duangpan Ratinan Boonklurb Matinee Juytai |
| author_facet | Ampol Duangpan Ratinan Boonklurb Matinee Juytai |
| author_sort | Ampol Duangpan |
| collection | DOAJ |
| description | In this paper, the finite integration method and the operational matrix of fractional integration are implemented based on the shifted Chebyshev polynomial. They are utilized to devise two numerical procedures for solving the systems of fractional and classical integro-differential equations. The fractional derivatives are described in the Caputo sense. The devised procedure can be successfully applied to solve the stiff system of ODEs. To demonstrate the efficiency, accuracy and numerical convergence order of these procedures, several experimental examples are given. As a consequence, the numerical computations illustrate that our presented procedures achieve significant improvement in terms of accuracy with less computational cost. |
| first_indexed | 2024-03-10T07:39:19Z |
| format | Article |
| id | doaj.art-13bd4cad820342d6902109bb4b2475a0 |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-10T07:39:19Z |
| publishDate | 2021-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-13bd4cad820342d6902109bb4b2475a02023-11-22T13:09:38ZengMDPI AGFractal and Fractional2504-31102021-08-015310310.3390/fractalfract5030103Numerical Solutions for Systems of Fractional and Classical Integro-Differential Equations via Finite Integration Method Based on Shifted Chebyshev PolynomialsAmpol Duangpan0Ratinan Boonklurb1Matinee Juytai2Department of Mathematics and Computer Science, Faculty of Science, Chulalongkorn University, Bangkok 10330, ThailandDepartment of Mathematics and Computer Science, Faculty of Science, Chulalongkorn University, Bangkok 10330, ThailandWinitsuksa School, Lopburi 15000, ThailandIn this paper, the finite integration method and the operational matrix of fractional integration are implemented based on the shifted Chebyshev polynomial. They are utilized to devise two numerical procedures for solving the systems of fractional and classical integro-differential equations. The fractional derivatives are described in the Caputo sense. The devised procedure can be successfully applied to solve the stiff system of ODEs. To demonstrate the efficiency, accuracy and numerical convergence order of these procedures, several experimental examples are given. As a consequence, the numerical computations illustrate that our presented procedures achieve significant improvement in terms of accuracy with less computational cost.https://www.mdpi.com/2504-3110/5/3/103finite integration methodshifted Chebyshev polynomialCaputo fractional derivativesystem of fractional integro-differential equationssystem of classical integro-differential equations |
| spellingShingle | Ampol Duangpan Ratinan Boonklurb Matinee Juytai Numerical Solutions for Systems of Fractional and Classical Integro-Differential Equations via Finite Integration Method Based on Shifted Chebyshev Polynomials Fractal and Fractional finite integration method shifted Chebyshev polynomial Caputo fractional derivative system of fractional integro-differential equations system of classical integro-differential equations |
| title | Numerical Solutions for Systems of Fractional and Classical Integro-Differential Equations via Finite Integration Method Based on Shifted Chebyshev Polynomials |
| title_full | Numerical Solutions for Systems of Fractional and Classical Integro-Differential Equations via Finite Integration Method Based on Shifted Chebyshev Polynomials |
| title_fullStr | Numerical Solutions for Systems of Fractional and Classical Integro-Differential Equations via Finite Integration Method Based on Shifted Chebyshev Polynomials |
| title_full_unstemmed | Numerical Solutions for Systems of Fractional and Classical Integro-Differential Equations via Finite Integration Method Based on Shifted Chebyshev Polynomials |
| title_short | Numerical Solutions for Systems of Fractional and Classical Integro-Differential Equations via Finite Integration Method Based on Shifted Chebyshev Polynomials |
| title_sort | numerical solutions for systems of fractional and classical integro differential equations via finite integration method based on shifted chebyshev polynomials |
| topic | finite integration method shifted Chebyshev polynomial Caputo fractional derivative system of fractional integro-differential equations system of classical integro-differential equations |
| url | https://www.mdpi.com/2504-3110/5/3/103 |
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