Bivariate Chebyshev Polynomials to Solve Time-Fractional Linear and Nonlinear KdV Equations
This work concerns the numerical solutions of a category of nonlinear and linear time-fractional partial differential equations (TFPDEs) that are called time-fractional inhomogeneous KdV and nonlinear time-fractional KdV equations, respectively. The fractional derivative operators are of the Caputo...
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2022/6554221 |
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| author | Azam Zahrani Mashaallah Matinfar Mostafa Eslami |
| author_facet | Azam Zahrani Mashaallah Matinfar Mostafa Eslami |
| author_sort | Azam Zahrani |
| collection | DOAJ |
| description | This work concerns the numerical solutions of a category of nonlinear and linear time-fractional partial differential equations (TFPDEs) that are called time-fractional inhomogeneous KdV and nonlinear time-fractional KdV equations, respectively. The fractional derivative operators are of the Caputo type. Two-variable second-kind Chebyshev wavelets (SKCWs) are constructed using one-variable ones; then, utilizing corresponding integral operational matrices leads to an approximate solution to the problem under study. Also, it is found that the perturbation term tends to zero even if a finite number of the basis functions is adopted. To exhibit the applicability and efficiency of the proposed scheme, two models of the KdV equations are given. |
| format | Article |
| id | doaj-art-fcb6c12ae6c9440884e25e86de8637d8 |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-fcb6c12ae6c9440884e25e86de8637d82025-02-03T06:00:27ZengWileyJournal of Mathematics2314-47852022-01-01202210.1155/2022/6554221Bivariate Chebyshev Polynomials to Solve Time-Fractional Linear and Nonlinear KdV EquationsAzam Zahrani0Mashaallah Matinfar1Mostafa Eslami2Department of MathematicsDepartment of MathematicsDepartment of MathematicsThis work concerns the numerical solutions of a category of nonlinear and linear time-fractional partial differential equations (TFPDEs) that are called time-fractional inhomogeneous KdV and nonlinear time-fractional KdV equations, respectively. The fractional derivative operators are of the Caputo type. Two-variable second-kind Chebyshev wavelets (SKCWs) are constructed using one-variable ones; then, utilizing corresponding integral operational matrices leads to an approximate solution to the problem under study. Also, it is found that the perturbation term tends to zero even if a finite number of the basis functions is adopted. To exhibit the applicability and efficiency of the proposed scheme, two models of the KdV equations are given.http://dx.doi.org/10.1155/2022/6554221 |
| spellingShingle | Azam Zahrani Mashaallah Matinfar Mostafa Eslami Bivariate Chebyshev Polynomials to Solve Time-Fractional Linear and Nonlinear KdV Equations Journal of Mathematics |
| title | Bivariate Chebyshev Polynomials to Solve Time-Fractional Linear and Nonlinear KdV Equations |
| title_full | Bivariate Chebyshev Polynomials to Solve Time-Fractional Linear and Nonlinear KdV Equations |
| title_fullStr | Bivariate Chebyshev Polynomials to Solve Time-Fractional Linear and Nonlinear KdV Equations |
| title_full_unstemmed | Bivariate Chebyshev Polynomials to Solve Time-Fractional Linear and Nonlinear KdV Equations |
| title_short | Bivariate Chebyshev Polynomials to Solve Time-Fractional Linear and Nonlinear KdV Equations |
| title_sort | bivariate chebyshev polynomials to solve time fractional linear and nonlinear kdv equations |
| url | http://dx.doi.org/10.1155/2022/6554221 |
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