Alternative Legendre Polynomials Method for Nonlinear Fractional Integro-Differential Equations with Weakly Singular Kernel
In this paper, we present a numerical scheme for finding numerical solution of a class of weakly singular nonlinear fractional integro-differential equations. This method exploits the alternative Legendre polynomials. An operational matrix, based on the alternative Legendre polynomials, is derived t...
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2021/9968237 |
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| _version_ | 1832566389956673536 |
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| author | Guodong Shi Yanlei Gong Mingxu Yi |
| author_facet | Guodong Shi Yanlei Gong Mingxu Yi |
| author_sort | Guodong Shi |
| collection | DOAJ |
| description | In this paper, we present a numerical scheme for finding numerical solution of a class of weakly singular nonlinear fractional integro-differential equations. This method exploits the alternative Legendre polynomials. An operational matrix, based on the alternative Legendre polynomials, is derived to be approximated the singular kernels of this class of the equations. The operational matrices of integration and product together with the derived operational matrix are utilized to transform nonlinear fractional integro-differential equations to the nonlinear system of algebraic equations. Furthermore, the proposed method has also been analyzed for convergence, particularly in context of error analysis. Moreover, results of essential numerical applications have also been documented in a graphical as well as tabular form to elaborate the effectiveness and accuracy of the proposed method. |
| format | Article |
| id | doaj-art-1be2c6ade93f4f3381ae1b74f5316300 |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-1be2c6ade93f4f3381ae1b74f53163002025-02-03T01:04:10ZengWileyJournal of Mathematics2314-46292314-47852021-01-01202110.1155/2021/99682379968237Alternative Legendre Polynomials Method for Nonlinear Fractional Integro-Differential Equations with Weakly Singular KernelGuodong Shi0Yanlei Gong1Mingxu Yi2School of Finance, Shanghai University of Finance and Economics, Shanghai 200433, ChinaSchool of Finance, Shanghai University of Finance and Economics, Shanghai 200433, ChinaSchool of Aeronautic Science and Technology, Beihang University, Beijing 100191, ChinaIn this paper, we present a numerical scheme for finding numerical solution of a class of weakly singular nonlinear fractional integro-differential equations. This method exploits the alternative Legendre polynomials. An operational matrix, based on the alternative Legendre polynomials, is derived to be approximated the singular kernels of this class of the equations. The operational matrices of integration and product together with the derived operational matrix are utilized to transform nonlinear fractional integro-differential equations to the nonlinear system of algebraic equations. Furthermore, the proposed method has also been analyzed for convergence, particularly in context of error analysis. Moreover, results of essential numerical applications have also been documented in a graphical as well as tabular form to elaborate the effectiveness and accuracy of the proposed method.http://dx.doi.org/10.1155/2021/9968237 |
| spellingShingle | Guodong Shi Yanlei Gong Mingxu Yi Alternative Legendre Polynomials Method for Nonlinear Fractional Integro-Differential Equations with Weakly Singular Kernel Journal of Mathematics |
| title | Alternative Legendre Polynomials Method for Nonlinear Fractional Integro-Differential Equations with Weakly Singular Kernel |
| title_full | Alternative Legendre Polynomials Method for Nonlinear Fractional Integro-Differential Equations with Weakly Singular Kernel |
| title_fullStr | Alternative Legendre Polynomials Method for Nonlinear Fractional Integro-Differential Equations with Weakly Singular Kernel |
| title_full_unstemmed | Alternative Legendre Polynomials Method for Nonlinear Fractional Integro-Differential Equations with Weakly Singular Kernel |
| title_short | Alternative Legendre Polynomials Method for Nonlinear Fractional Integro-Differential Equations with Weakly Singular Kernel |
| title_sort | alternative legendre polynomials method for nonlinear fractional integro differential equations with weakly singular kernel |
| url | http://dx.doi.org/10.1155/2021/9968237 |
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