New Numerical Results on Existence of Volterra–Fredholm Integral Equation of Nonlinear Boundary Integro-Differential Type
Symmetry is presented in many works involving differential and integral equations. Whenever a human is involved in the design of an integral equation, they naturally tend to opt for symmetric features. The most common examples are the Green functions and linguistic kernels that are often designed sy...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-05-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/15/6/1144 |
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| author | Hawsar HamaRashid Hari Mohan Srivastava Mudhafar Hama Pshtiwan Othman Mohammed Eman Al-Sarairah Musawa Yahya Almusawa |
| author_facet | Hawsar HamaRashid Hari Mohan Srivastava Mudhafar Hama Pshtiwan Othman Mohammed Eman Al-Sarairah Musawa Yahya Almusawa |
| author_sort | Hawsar HamaRashid |
| collection | DOAJ |
| description | Symmetry is presented in many works involving differential and integral equations. Whenever a human is involved in the design of an integral equation, they naturally tend to opt for symmetric features. The most common examples are the Green functions and linguistic kernels that are often designed symmetrically and regularly distributed over the universe of discourse. In the current study, the authors report a study on boundary value problem (BVP) for a nonlinear integro Volterra–Fredholm integral equation with variable coefficients and show the existence of solution by applying some fixed-point theorems. The authors employ various numerical common approaches as the homotopy analysis methodology established by Liao and the modified Adomain decomposition technique to produce a numerical approximate solution, then graphical depiction reveals that both methods are most effective and convenient. In this regard, the authors address the requirements that ensure the existence and uniqueness of the solution for various variations of nonlinearity power. The authors also show numerical examples of how to apply our primary theorems and test the convergence and validity of our suggested approach. |
| first_indexed | 2024-03-11T01:53:17Z |
| format | Article |
| id | doaj.art-9e78b9942f754d3e997f16f3e35ae2ee |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-11T01:53:17Z |
| publishDate | 2023-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-9e78b9942f754d3e997f16f3e35ae2ee2023-11-18T12:50:03ZengMDPI AGSymmetry2073-89942023-05-01156114410.3390/sym15061144New Numerical Results on Existence of Volterra–Fredholm Integral Equation of Nonlinear Boundary Integro-Differential TypeHawsar HamaRashid0Hari Mohan Srivastava1Mudhafar Hama2Pshtiwan Othman Mohammed3Eman Al-Sarairah4Musawa Yahya Almusawa5Department of Mathematics, College of Education, University of Sulaimani, Sulaimani 46001, Kurdistan Region, IraqDepartment of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3R4, CanadaDepartment of Mathematics, College of Science, University of Sulaimani, Sulaimani 46001, Kurdistan Region, IraqDepartment of Mathematics, College of Education, University of Sulaimani, Sulaimani 46001, Kurdistan Region, IraqDepartment of Mathematics, Khalifa University, Abu Dhabi P.O. Box 127788, United Arab EmiratesDepartment of Mathematics, Faculty of Science, Jazan University, Jazan 45142, Saudi ArabiaSymmetry is presented in many works involving differential and integral equations. Whenever a human is involved in the design of an integral equation, they naturally tend to opt for symmetric features. The most common examples are the Green functions and linguistic kernels that are often designed symmetrically and regularly distributed over the universe of discourse. In the current study, the authors report a study on boundary value problem (BVP) for a nonlinear integro Volterra–Fredholm integral equation with variable coefficients and show the existence of solution by applying some fixed-point theorems. The authors employ various numerical common approaches as the homotopy analysis methodology established by Liao and the modified Adomain decomposition technique to produce a numerical approximate solution, then graphical depiction reveals that both methods are most effective and convenient. In this regard, the authors address the requirements that ensure the existence and uniqueness of the solution for various variations of nonlinearity power. The authors also show numerical examples of how to apply our primary theorems and test the convergence and validity of our suggested approach.https://www.mdpi.com/2073-8994/15/6/1144boundary conditionsnonlinear integro-differential equationsKrasnoselskii fixed point theoremArzela–Ascoli theorem |
| spellingShingle | Hawsar HamaRashid Hari Mohan Srivastava Mudhafar Hama Pshtiwan Othman Mohammed Eman Al-Sarairah Musawa Yahya Almusawa New Numerical Results on Existence of Volterra–Fredholm Integral Equation of Nonlinear Boundary Integro-Differential Type Symmetry boundary conditions nonlinear integro-differential equations Krasnoselskii fixed point theorem Arzela–Ascoli theorem |
| title | New Numerical Results on Existence of Volterra–Fredholm Integral Equation of Nonlinear Boundary Integro-Differential Type |
| title_full | New Numerical Results on Existence of Volterra–Fredholm Integral Equation of Nonlinear Boundary Integro-Differential Type |
| title_fullStr | New Numerical Results on Existence of Volterra–Fredholm Integral Equation of Nonlinear Boundary Integro-Differential Type |
| title_full_unstemmed | New Numerical Results on Existence of Volterra–Fredholm Integral Equation of Nonlinear Boundary Integro-Differential Type |
| title_short | New Numerical Results on Existence of Volterra–Fredholm Integral Equation of Nonlinear Boundary Integro-Differential Type |
| title_sort | new numerical results on existence of volterra fredholm integral equation of nonlinear boundary integro differential type |
| topic | boundary conditions nonlinear integro-differential equations Krasnoselskii fixed point theorem Arzela–Ascoli theorem |
| url | https://www.mdpi.com/2073-8994/15/6/1144 |
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