New algorithms for solving nonlinear mixed integral equations
In this article, the existence and unique solution of the nonlinear Volterra-Fredholm integral equation (NVFIE) of the second kind is discussed. We also prove the solvability of the second kind of the NVFIE using the Banach fixed point theorem. Using quadrature method, the NVFIE leads to a system of...
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| Format: | Article |
| Language: | English |
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AIMS Press
2023-09-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.20231406?viewType=HTML |
| _version_ | 1797652609351286784 |
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| author | R. T. Matoog M. A. Abdou M. A. Abdel-Aty |
| author_facet | R. T. Matoog M. A. Abdou M. A. Abdel-Aty |
| author_sort | R. T. Matoog |
| collection | DOAJ |
| description | In this article, the existence and unique solution of the nonlinear Volterra-Fredholm integral equation (NVFIE) of the second kind is discussed. We also prove the solvability of the second kind of the NVFIE using the Banach fixed point theorem. Using quadrature method, the NVFIE leads to a system of nonlinear Fredholm integral equations (NFIEs). The existence and unique numerical solution of this system is discussed. Then, the modified Taylor's method was applied to transform the system of NFIEs into nonlinear algebraic systems (NAS). The existence and uniqueness of the nonlinear algebraic system's solution are discussed using Banach's fixed point theorem. Also, the stability of the modified error is presented. Some numerical examples are performed to show the efficiency and simplicity of the presented method, and all results are obtained using Wolfram Mathematica 11. |
| first_indexed | 2024-03-11T16:32:29Z |
| format | Article |
| id | doaj.art-b37da27f036f42449aca7c87f0767118 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-03-11T16:32:29Z |
| publishDate | 2023-09-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-b37da27f036f42449aca7c87f07671182023-10-24T01:21:22ZengAIMS PressAIMS Mathematics2473-69882023-09-01811274882751210.3934/math.20231406New algorithms for solving nonlinear mixed integral equationsR. T. Matoog 0M. A. Abdou1M. A. Abdel-Aty21. Department of Mathematics, Faculty of Applied Sciences, Umm Al–Qura University, Makkah, Saudi Arabia2. Department of Mathematics, Faculty of Education, Alexandria University, Alexandria 21511, Egypt3. Department of Mathematics, Faculty of Science, Benha University, Benha 13518, EgyptIn this article, the existence and unique solution of the nonlinear Volterra-Fredholm integral equation (NVFIE) of the second kind is discussed. We also prove the solvability of the second kind of the NVFIE using the Banach fixed point theorem. Using quadrature method, the NVFIE leads to a system of nonlinear Fredholm integral equations (NFIEs). The existence and unique numerical solution of this system is discussed. Then, the modified Taylor's method was applied to transform the system of NFIEs into nonlinear algebraic systems (NAS). The existence and uniqueness of the nonlinear algebraic system's solution are discussed using Banach's fixed point theorem. Also, the stability of the modified error is presented. Some numerical examples are performed to show the efficiency and simplicity of the presented method, and all results are obtained using Wolfram Mathematica 11.https://www.aimspress.com/article/doi/10.3934/math.20231406?viewType=HTMLpicard's methodnonlinear volterra-fredholm integral equationbanach fixed point theoremsystem of nonlinear fredholm integral equationsnonlinear algebraic systemmodified taylor's method |
| spellingShingle | R. T. Matoog M. A. Abdou M. A. Abdel-Aty New algorithms for solving nonlinear mixed integral equations AIMS Mathematics picard's method nonlinear volterra-fredholm integral equation banach fixed point theorem system of nonlinear fredholm integral equations nonlinear algebraic system modified taylor's method |
| title | New algorithms for solving nonlinear mixed integral equations |
| title_full | New algorithms for solving nonlinear mixed integral equations |
| title_fullStr | New algorithms for solving nonlinear mixed integral equations |
| title_full_unstemmed | New algorithms for solving nonlinear mixed integral equations |
| title_short | New algorithms for solving nonlinear mixed integral equations |
| title_sort | new algorithms for solving nonlinear mixed integral equations |
| topic | picard's method nonlinear volterra-fredholm integral equation banach fixed point theorem system of nonlinear fredholm integral equations nonlinear algebraic system modified taylor's method |
| url | https://www.aimspress.com/article/doi/10.3934/math.20231406?viewType=HTML |
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