An efficient technique based on least-squares method for fractional integro-differential equations
In this paper, we investigate an efficient technique for solving fractional integro-differential equations (FIDEs) that have numerous applications in various fields of science. The proposed technique is based upon the Legendre orthonormal polynomial and least Csquares method (LSM). By dividing the d...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Elsevier
2023-02-01
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| Series: | Alexandria Engineering Journal |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S1110016822005634 |
| _version_ | 1797961122587869184 |
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| author | Yuntao Jia Minqiang Xu Yingzhen Lin Danhua Jiang |
| author_facet | Yuntao Jia Minqiang Xu Yingzhen Lin Danhua Jiang |
| author_sort | Yuntao Jia |
| collection | DOAJ |
| description | In this paper, we investigate an efficient technique for solving fractional integro-differential equations (FIDEs) that have numerous applications in various fields of science. The proposed technique is based upon the Legendre orthonormal polynomial and least Csquares method (LSM). By dividing the domain into n cells, a k-th order polynomial approximate solution in each cell can be obtained by LSM. The unique solvability and stability of the proposed numerical scheme are proven by analyzing the condition number of the matrix of the linear system. Moreover, the optimal convergence order under W22–norm is provided as well. Numerical examples are studied to verify our theoretical discovery. Comparison with the traditional reproducing kernel method and C3-spline method illustrates that our algorithm can obtain a more accurate approximating solution. |
| first_indexed | 2024-04-11T00:54:28Z |
| format | Article |
| id | doaj.art-74d5efb168814f23b5b35a8e94b89e4c |
| institution | Directory Open Access Journal |
| issn | 1110-0168 |
| language | English |
| last_indexed | 2024-04-11T00:54:28Z |
| publishDate | 2023-02-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Alexandria Engineering Journal |
| spelling | doaj.art-74d5efb168814f23b5b35a8e94b89e4c2023-01-05T06:46:07ZengElsevierAlexandria Engineering Journal1110-01682023-02-016497105An efficient technique based on least-squares method for fractional integro-differential equationsYuntao Jia0Minqiang Xu1Yingzhen Lin2Danhua Jiang3School of Science, Zhuhai Campus, Beijing Institute of Technology, Zhuhai, Guangdong 519085, ChinaCollege of Science, Zhejiang University of Technology, Hangzhou 310014, ChinaSchool of Science, Zhuhai Campus, Beijing Institute of Technology, Zhuhai, Guangdong 519085, ChinaCollege of Science, Zhejiang University of Technology, Hangzhou 310014, ChinaIn this paper, we investigate an efficient technique for solving fractional integro-differential equations (FIDEs) that have numerous applications in various fields of science. The proposed technique is based upon the Legendre orthonormal polynomial and least Csquares method (LSM). By dividing the domain into n cells, a k-th order polynomial approximate solution in each cell can be obtained by LSM. The unique solvability and stability of the proposed numerical scheme are proven by analyzing the condition number of the matrix of the linear system. Moreover, the optimal convergence order under W22–norm is provided as well. Numerical examples are studied to verify our theoretical discovery. Comparison with the traditional reproducing kernel method and C3-spline method illustrates that our algorithm can obtain a more accurate approximating solution.http://www.sciencedirect.com/science/article/pii/S1110016822005634FIDEsLSMStabilityOptimal convergence order |
| spellingShingle | Yuntao Jia Minqiang Xu Yingzhen Lin Danhua Jiang An efficient technique based on least-squares method for fractional integro-differential equations Alexandria Engineering Journal FIDEs LSM Stability Optimal convergence order |
| title | An efficient technique based on least-squares method for fractional integro-differential equations |
| title_full | An efficient technique based on least-squares method for fractional integro-differential equations |
| title_fullStr | An efficient technique based on least-squares method for fractional integro-differential equations |
| title_full_unstemmed | An efficient technique based on least-squares method for fractional integro-differential equations |
| title_short | An efficient technique based on least-squares method for fractional integro-differential equations |
| title_sort | efficient technique based on least squares method for fractional integro differential equations |
| topic | FIDEs LSM Stability Optimal convergence order |
| url | http://www.sciencedirect.com/science/article/pii/S1110016822005634 |
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