A spectral collocation method for solving stochastic fractional integro-differential equation
In this paper, a numerical scheme based on shifted Vieta-Lucas polynomials is utilised to solve mentioned equation. The main characteristic of the presented method is to approximate Brownian motion with help of the Gauss-Legendre quadrature, which makes calculations easier. Another character...
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Qom University of Technology
2025-06-01
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| Series: | Mathematics and Computational Sciences |
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| Online Access: | https://mcs.qut.ac.ir/article_721358_5de3fbd101655e0cc834cb8d33d42469.pdf |
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| author | Mahsa Zaboli Haleh Tajadodi |
| author_facet | Mahsa Zaboli Haleh Tajadodi |
| author_sort | Mahsa Zaboli |
| collection | DOAJ |
| description | In this paper, a numerical scheme based on shifted Vieta-Lucas polynomials is utilised to solve mentioned equation. The main characteristic of the presented method is to approximate Brownian motion with help of the Gauss-Legendre quadrature, which makes calculations easier. Another characteristic of this method are employed suitable collocation points to convert the stochastic equation under the study into a system of algebraic equations by using the operational matrices. So that, Newton's method is applied to solve them. The convergence analysis and error bound of the suggested method are well established. Additionally, the proofs related to the existence and uniqueness of the solutions for the equations under investigation have been provided. In order to illustrate the effectiveness, compatibility and plausibility of the proposed technique, four numerical examples are presented. |
| format | Article |
| id | doaj-art-2c6c7ad2014d423e8535de27a3ae38ff |
| institution | Kabale University |
| issn | 2717-2708 |
| language | English |
| publishDate | 2025-06-01 |
| publisher | Qom University of Technology |
| record_format | Article |
| series | Mathematics and Computational Sciences |
| spelling | doaj-art-2c6c7ad2014d423e8535de27a3ae38ff2025-08-20T03:33:15ZengQom University of TechnologyMathematics and Computational Sciences2717-27082025-06-016213110.30511/mcs.2025.2037499.1218721358A spectral collocation method for solving stochastic fractional integro-differential equationMahsa Zaboli0Haleh Tajadodi1Department of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran.Department of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran.In this paper, a numerical scheme based on shifted Vieta-Lucas polynomials is utilised to solve mentioned equation. The main characteristic of the presented method is to approximate Brownian motion with help of the Gauss-Legendre quadrature, which makes calculations easier. Another characteristic of this method are employed suitable collocation points to convert the stochastic equation under the study into a system of algebraic equations by using the operational matrices. So that, Newton's method is applied to solve them. The convergence analysis and error bound of the suggested method are well established. Additionally, the proofs related to the existence and uniqueness of the solutions for the equations under investigation have been provided. In order to illustrate the effectiveness, compatibility and plausibility of the proposed technique, four numerical examples are presented.https://mcs.qut.ac.ir/article_721358_5de3fbd101655e0cc834cb8d33d42469.pdfstochastic fractional integro-differential equationsshifted vieta-lucas polynomialsoperational matrixbrownian motion |
| spellingShingle | Mahsa Zaboli Haleh Tajadodi A spectral collocation method for solving stochastic fractional integro-differential equation Mathematics and Computational Sciences stochastic fractional integro-differential equations shifted vieta-lucas polynomials operational matrix brownian motion |
| title | A spectral collocation method for solving stochastic fractional integro-differential equation |
| title_full | A spectral collocation method for solving stochastic fractional integro-differential equation |
| title_fullStr | A spectral collocation method for solving stochastic fractional integro-differential equation |
| title_full_unstemmed | A spectral collocation method for solving stochastic fractional integro-differential equation |
| title_short | A spectral collocation method for solving stochastic fractional integro-differential equation |
| title_sort | a spectral collocation method for solving stochastic fractional integro differential equation |
| topic | stochastic fractional integro-differential equations shifted vieta-lucas polynomials operational matrix brownian motion |
| url | https://mcs.qut.ac.ir/article_721358_5de3fbd101655e0cc834cb8d33d42469.pdf |
| work_keys_str_mv | AT mahsazaboli aspectralcollocationmethodforsolvingstochasticfractionalintegrodifferentialequation AT halehtajadodi aspectralcollocationmethodforsolvingstochasticfractionalintegrodifferentialequation |