Numerical Solution for the 2D Linear Fredholm Functional Integral Equations
In this work, a numerical method is applied for obtaining numerical solutions of Fredholm two-dimensional functional linear integral equations based on the radial basis function (RBF). To find the approximate solutions of these types of equations, first, we approximate the unknown function as a fini...
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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/10.1155/2021/9560595 |
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| author | Neda Khaksari Mahmoud Paripour Nasrin Karamikabir |
| author_facet | Neda Khaksari Mahmoud Paripour Nasrin Karamikabir |
| author_sort | Neda Khaksari |
| collection | DOAJ |
| description | In this work, a numerical method is applied for obtaining numerical solutions of Fredholm two-dimensional functional linear integral equations based on the radial basis function (RBF). To find the approximate solutions of these types of equations, first, we approximate the unknown function as a finite series in terms of basic functions. Then, by using the proposed method, we give a formula for determining the unknown function. Using this formula, we obtain a numerical method for solving Fredholm two-dimensional functional linear integral equations. Using the proposed method, we get a system of linear algebraic equations which are solved by an iteration method. In the end, the accuracy and applicability of the proposed method are shown through some numerical applications. |
| format | Article |
| id | doaj-art-2e77973ceb804763990852b66fdc98e0 |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-2e77973ceb804763990852b66fdc98e02025-02-03T05:57:20ZengWileyJournal of Mathematics2314-47852021-01-01202110.1155/2021/9560595Numerical Solution for the 2D Linear Fredholm Functional Integral EquationsNeda Khaksari0Mahmoud Paripour1Nasrin Karamikabir2Department of MathematicsDepartment of Computer Engineering and Information TechnologyDepartment of MathematicsIn this work, a numerical method is applied for obtaining numerical solutions of Fredholm two-dimensional functional linear integral equations based on the radial basis function (RBF). To find the approximate solutions of these types of equations, first, we approximate the unknown function as a finite series in terms of basic functions. Then, by using the proposed method, we give a formula for determining the unknown function. Using this formula, we obtain a numerical method for solving Fredholm two-dimensional functional linear integral equations. Using the proposed method, we get a system of linear algebraic equations which are solved by an iteration method. In the end, the accuracy and applicability of the proposed method are shown through some numerical applications.http://dx.doi.org/10.1155/2021/9560595 |
| spellingShingle | Neda Khaksari Mahmoud Paripour Nasrin Karamikabir Numerical Solution for the 2D Linear Fredholm Functional Integral Equations Journal of Mathematics |
| title | Numerical Solution for the 2D Linear Fredholm Functional Integral Equations |
| title_full | Numerical Solution for the 2D Linear Fredholm Functional Integral Equations |
| title_fullStr | Numerical Solution for the 2D Linear Fredholm Functional Integral Equations |
| title_full_unstemmed | Numerical Solution for the 2D Linear Fredholm Functional Integral Equations |
| title_short | Numerical Solution for the 2D Linear Fredholm Functional Integral Equations |
| title_sort | numerical solution for the 2d linear fredholm functional integral equations |
| url | http://dx.doi.org/10.1155/2021/9560595 |
| work_keys_str_mv | AT nedakhaksari numericalsolutionforthe2dlinearfredholmfunctionalintegralequations AT mahmoudparipour numericalsolutionforthe2dlinearfredholmfunctionalintegralequations AT nasrinkaramikabir numericalsolutionforthe2dlinearfredholmfunctionalintegralequations |