Nonlinear Fredholm integro-differential equation in two-dimensional and its numerical solutions
This paper proposes a new definition of the nonlinear Fredholm integro-differential equation of the second kind with continuous kernel in two-dimensional (NT-DFIDE). Furthermore, the work is concerned to study this new equation numerically. The existence of a unique solution of the equation is prove...
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| Format: | Article |
| Language: | English |
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AIMS Press
2021-07-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2021602?viewType=HTML |
| _version_ | 1818652517954748416 |
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| author | A. M. Al-Bugami |
| author_facet | A. M. Al-Bugami |
| author_sort | A. M. Al-Bugami |
| collection | DOAJ |
| description | This paper proposes a new definition of the nonlinear Fredholm integro-differential equation of the second kind with continuous kernel in two-dimensional (NT-DFIDE). Furthermore, the work is concerned to study this new equation numerically. The existence of a unique solution of the equation is proved. In addition, the approximate solutions of NT-DFIDE are obtained by two powerful methods Adomian Decomposition Method (ADM) and Homotopy Analysis Method (HAM). The given numerical examples showed the efficiency and accuracy of the introduced methods. |
| first_indexed | 2024-12-17T02:23:16Z |
| format | Article |
| id | doaj.art-2d6deae39a15434dade95f7214ab4820 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-12-17T02:23:16Z |
| publishDate | 2021-07-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-2d6deae39a15434dade95f7214ab48202022-12-21T22:07:12ZengAIMS PressAIMS Mathematics2473-69882021-07-01610103831039410.3934/math.2021602Nonlinear Fredholm integro-differential equation in two-dimensional and its numerical solutionsA. M. Al-Bugami0Department of Mathematics, Faculty of Sciences Taif University, Taif, Saudi ArabiaThis paper proposes a new definition of the nonlinear Fredholm integro-differential equation of the second kind with continuous kernel in two-dimensional (NT-DFIDE). Furthermore, the work is concerned to study this new equation numerically. The existence of a unique solution of the equation is proved. In addition, the approximate solutions of NT-DFIDE are obtained by two powerful methods Adomian Decomposition Method (ADM) and Homotopy Analysis Method (HAM). The given numerical examples showed the efficiency and accuracy of the introduced methods.https://www.aimspress.com/article/doi/10.3934/math.2021602?viewType=HTMLfredholm integro-differential equationadomian decompositionhomotopy analysis |
| spellingShingle | A. M. Al-Bugami Nonlinear Fredholm integro-differential equation in two-dimensional and its numerical solutions AIMS Mathematics fredholm integro-differential equation adomian decomposition homotopy analysis |
| title | Nonlinear Fredholm integro-differential equation in two-dimensional and its numerical solutions |
| title_full | Nonlinear Fredholm integro-differential equation in two-dimensional and its numerical solutions |
| title_fullStr | Nonlinear Fredholm integro-differential equation in two-dimensional and its numerical solutions |
| title_full_unstemmed | Nonlinear Fredholm integro-differential equation in two-dimensional and its numerical solutions |
| title_short | Nonlinear Fredholm integro-differential equation in two-dimensional and its numerical solutions |
| title_sort | nonlinear fredholm integro differential equation in two dimensional and its numerical solutions |
| topic | fredholm integro-differential equation adomian decomposition homotopy analysis |
| url | https://www.aimspress.com/article/doi/10.3934/math.2021602?viewType=HTML |
| work_keys_str_mv | AT amalbugami nonlinearfredholmintegrodifferentialequationintwodimensionalanditsnumericalsolutions |