Study of Nonlocal Boundary Value Problem for the Fredholm–Volterra Integro-Differential Equation
In this paper, the existence and uniqueness of the Fredholm–Volterra integro-differential equation with the nonlocal condition will be studied. Also, we study the continuous dependence of the initial data. The numerical solution of the problem will be studied using the central difference approximati...
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| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2022-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2022/4773005 |
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| _version_ | 1832565597366386688 |
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| author | K. R. Raslan Khalid K. Ali Reda Gamal Ahmed Hind K. Al-Jeaid Amira Abd-Elall Ibrahim |
| author_facet | K. R. Raslan Khalid K. Ali Reda Gamal Ahmed Hind K. Al-Jeaid Amira Abd-Elall Ibrahim |
| author_sort | K. R. Raslan |
| collection | DOAJ |
| description | In this paper, the existence and uniqueness of the Fredholm–Volterra integro-differential equation with the nonlocal condition will be studied. Also, we study the continuous dependence of the initial data. The numerical solution of the problem will be studied using the central difference approximations and trapezoidal rule to transform the Volterra–Fredholm integro-differential equation into a system of algebraic equations which can be solved together to get the solution. Finally, we solve some examples numerically to show the accuracy of the proposed method. |
| format | Article |
| id | doaj-art-9954323647bb446d8711628c1c38845c |
| institution | Kabale University |
| issn | 2314-8888 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-9954323647bb446d8711628c1c38845c2025-02-03T01:07:10ZengWileyJournal of Function Spaces2314-88882022-01-01202210.1155/2022/4773005Study of Nonlocal Boundary Value Problem for the Fredholm–Volterra Integro-Differential EquationK. R. Raslan0Khalid K. Ali1Reda Gamal Ahmed2Hind K. Al-Jeaid3Amira Abd-Elall Ibrahim4Department of MathematicsDepartment of MathematicsDepartment of MathematicsDepartment of Mathematical SciencesOctober High Institute for Engineering and TechnologyIn this paper, the existence and uniqueness of the Fredholm–Volterra integro-differential equation with the nonlocal condition will be studied. Also, we study the continuous dependence of the initial data. The numerical solution of the problem will be studied using the central difference approximations and trapezoidal rule to transform the Volterra–Fredholm integro-differential equation into a system of algebraic equations which can be solved together to get the solution. Finally, we solve some examples numerically to show the accuracy of the proposed method.http://dx.doi.org/10.1155/2022/4773005 |
| spellingShingle | K. R. Raslan Khalid K. Ali Reda Gamal Ahmed Hind K. Al-Jeaid Amira Abd-Elall Ibrahim Study of Nonlocal Boundary Value Problem for the Fredholm–Volterra Integro-Differential Equation Journal of Function Spaces |
| title | Study of Nonlocal Boundary Value Problem for the Fredholm–Volterra Integro-Differential Equation |
| title_full | Study of Nonlocal Boundary Value Problem for the Fredholm–Volterra Integro-Differential Equation |
| title_fullStr | Study of Nonlocal Boundary Value Problem for the Fredholm–Volterra Integro-Differential Equation |
| title_full_unstemmed | Study of Nonlocal Boundary Value Problem for the Fredholm–Volterra Integro-Differential Equation |
| title_short | Study of Nonlocal Boundary Value Problem for the Fredholm–Volterra Integro-Differential Equation |
| title_sort | study of nonlocal boundary value problem for the fredholm volterra integro differential equation |
| url | http://dx.doi.org/10.1155/2022/4773005 |
| work_keys_str_mv | AT krraslan studyofnonlocalboundaryvalueproblemforthefredholmvolterraintegrodifferentialequation AT khalidkali studyofnonlocalboundaryvalueproblemforthefredholmvolterraintegrodifferentialequation AT redagamalahmed studyofnonlocalboundaryvalueproblemforthefredholmvolterraintegrodifferentialequation AT hindkaljeaid studyofnonlocalboundaryvalueproblemforthefredholmvolterraintegrodifferentialequation AT amiraabdelallibrahim studyofnonlocalboundaryvalueproblemforthefredholmvolterraintegrodifferentialequation |