Numerical solution of nonlinear Volterra-Fredholm integral equations of the first kind using alternative Legendre polynomials
Alternative Legendre polynomials (ALPs) are used for approximating the solution of nonlinear Volterra-Fredholm integral equations (VFIEs) of the rst kind. The problem is rst transformed into a second kind VFIE and then, using the ALP operational matrices of integration and the product, the solution...
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| Format: | Article |
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Kharazmi University
2021-12-01
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| Series: | پژوهشهای ریاضی |
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| Online Access: | http://mmr.khu.ac.ir/article-1-2973-en.html |
| _version_ | 1797871644240248832 |
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| author | Sohrab Bazm Alireza Hosseini |
| author_facet | Sohrab Bazm Alireza Hosseini |
| author_sort | Sohrab Bazm |
| collection | DOAJ |
| description | Alternative Legendre polynomials (ALPs) are used for approximating the solution of nonlinear Volterra-Fredholm integral equations (VFIEs) of the rst kind. The problem is rst transformed into a second kind VFIE and then, using the ALP operational matrices of integration and the product, the solution of the later problem is reduced to the one of solving a system of nonlinear algebraic equations with unknown ALP coecients of the exact solution. An error analysis of the method is given. Results of numerical examples are presented, which illustrate that the proposed method achieve good accuracy even using a small number of ALPs.
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| first_indexed | 2024-04-10T00:47:06Z |
| format | Article |
| id | doaj.art-5458ffd925914519a21d6a172f4bd391 |
| institution | Directory Open Access Journal |
| issn | 2588-2546 2588-2554 |
| language | fas |
| last_indexed | 2024-04-10T00:47:06Z |
| publishDate | 2021-12-01 |
| publisher | Kharazmi University |
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| series | پژوهشهای ریاضی |
| spelling | doaj.art-5458ffd925914519a21d6a172f4bd3912023-03-13T19:23:00ZfasKharazmi Universityپژوهشهای ریاضی2588-25462588-25542021-12-0173443466Numerical solution of nonlinear Volterra-Fredholm integral equations of the first kind using alternative Legendre polynomialsSohrab Bazm0Alireza Hosseini1 University of Maragheh University of Tehran Alternative Legendre polynomials (ALPs) are used for approximating the solution of nonlinear Volterra-Fredholm integral equations (VFIEs) of the rst kind. The problem is rst transformed into a second kind VFIE and then, using the ALP operational matrices of integration and the product, the solution of the later problem is reduced to the one of solving a system of nonlinear algebraic equations with unknown ALP coecients of the exact solution. An error analysis of the method is given. Results of numerical examples are presented, which illustrate that the proposed method achieve good accuracy even using a small number of ALPs. ./files/site1/files/%D8%A8%D8%B2%D9%85.pdfhttp://mmr.khu.ac.ir/article-1-2973-en.htmlnonlinear integral equations of the first kindvolterra-fredholm integral equationsalternative legendre polynomialsoperational matrix |
| spellingShingle | Sohrab Bazm Alireza Hosseini Numerical solution of nonlinear Volterra-Fredholm integral equations of the first kind using alternative Legendre polynomials پژوهشهای ریاضی nonlinear integral equations of the first kind volterra-fredholm integral equations alternative legendre polynomials operational matrix |
| title | Numerical solution of nonlinear Volterra-Fredholm integral equations of the first kind using alternative Legendre polynomials |
| title_full | Numerical solution of nonlinear Volterra-Fredholm integral equations of the first kind using alternative Legendre polynomials |
| title_fullStr | Numerical solution of nonlinear Volterra-Fredholm integral equations of the first kind using alternative Legendre polynomials |
| title_full_unstemmed | Numerical solution of nonlinear Volterra-Fredholm integral equations of the first kind using alternative Legendre polynomials |
| title_short | Numerical solution of nonlinear Volterra-Fredholm integral equations of the first kind using alternative Legendre polynomials |
| title_sort | numerical solution of nonlinear volterra fredholm integral equations of the first kind using alternative legendre polynomials |
| topic | nonlinear integral equations of the first kind volterra-fredholm integral equations alternative legendre polynomials operational matrix |
| url | http://mmr.khu.ac.ir/article-1-2973-en.html |
| work_keys_str_mv | AT sohrabbazm numericalsolutionofnonlinearvolterrafredholmintegralequationsofthefirstkindusingalternativelegendrepolynomials AT alirezahosseini numericalsolutionofnonlinearvolterrafredholmintegralequationsofthefirstkindusingalternativelegendrepolynomials |