Generalized Auto-Convolution Volterra Integral Equations: Numerical Treatments
In this paper, we use the operational Tau method based on orthogonal polynomials to achieve a numerical solution of generalized autoconvolution Volterra integral equations. Displaying a lower triangular matrix for basis functions, the corresponding solution is represented in matrix form, and an infi...
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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/10.1155/2022/4867066 |
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| author | Mahdi Namazi Nezamabadi Saeed Pishbin |
| author_facet | Mahdi Namazi Nezamabadi Saeed Pishbin |
| author_sort | Mahdi Namazi Nezamabadi |
| collection | DOAJ |
| description | In this paper, we use the operational Tau method based on orthogonal polynomials to achieve a numerical solution of generalized autoconvolution Volterra integral equations. Displaying a lower triangular matrix for basis functions, the corresponding solution is represented in matrix form, and an infinite upper triangular Toeplitz matrix is used to show the matrix representation of the integral part of the autoconvolution integral equation. We also investigate solvability of the obtained nonlinear system with infinite dimensional space and examine the convergence analysis of this method under the L2− norm. Finally, the efficiency of the operational Tau method is studied by numerical examples. |
| format | Article |
| id | doaj-art-49e0bd9a92dc4f8b8d9aa626a2671939 |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-49e0bd9a92dc4f8b8d9aa626a26719392025-02-03T06:12:25ZengWileyJournal of Mathematics2314-47852022-01-01202210.1155/2022/4867066Generalized Auto-Convolution Volterra Integral Equations: Numerical TreatmentsMahdi Namazi Nezamabadi0Saeed Pishbin1Department of MathematicsDepartment of MathematicsIn this paper, we use the operational Tau method based on orthogonal polynomials to achieve a numerical solution of generalized autoconvolution Volterra integral equations. Displaying a lower triangular matrix for basis functions, the corresponding solution is represented in matrix form, and an infinite upper triangular Toeplitz matrix is used to show the matrix representation of the integral part of the autoconvolution integral equation. We also investigate solvability of the obtained nonlinear system with infinite dimensional space and examine the convergence analysis of this method under the L2− norm. Finally, the efficiency of the operational Tau method is studied by numerical examples.http://dx.doi.org/10.1155/2022/4867066 |
| spellingShingle | Mahdi Namazi Nezamabadi Saeed Pishbin Generalized Auto-Convolution Volterra Integral Equations: Numerical Treatments Journal of Mathematics |
| title | Generalized Auto-Convolution Volterra Integral Equations: Numerical Treatments |
| title_full | Generalized Auto-Convolution Volterra Integral Equations: Numerical Treatments |
| title_fullStr | Generalized Auto-Convolution Volterra Integral Equations: Numerical Treatments |
| title_full_unstemmed | Generalized Auto-Convolution Volterra Integral Equations: Numerical Treatments |
| title_short | Generalized Auto-Convolution Volterra Integral Equations: Numerical Treatments |
| title_sort | generalized auto convolution volterra integral equations numerical treatments |
| url | http://dx.doi.org/10.1155/2022/4867066 |
| work_keys_str_mv | AT mahdinamazinezamabadi generalizedautoconvolutionvolterraintegralequationsnumericaltreatments AT saeedpishbin generalizedautoconvolutionvolterraintegralequationsnumericaltreatments |