Approximation Technique for Solving Linear Volterra Integro-Differential Equations with Boundary Conditions
This paper presents a new technique for solving linear Volterra integro-differential equations with boundary conditions. The method is based on the blending of the Chebyshev spectral methods. The application of the proposed method leads the Volterra integro-differential equation to a system of algeb...
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2022/2217882 |
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| _version_ | 1832545941324824576 |
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| author | Mohamed E. A. Alnair Ahmed A. Khidir |
| author_facet | Mohamed E. A. Alnair Ahmed A. Khidir |
| author_sort | Mohamed E. A. Alnair |
| collection | DOAJ |
| description | This paper presents a new technique for solving linear Volterra integro-differential equations with boundary conditions. The method is based on the blending of the Chebyshev spectral methods. The application of the proposed method leads the Volterra integro-differential equation to a system of algebraic equations that are easy to solve. Some examples are introduced and the obtained results are compared with exact solution as well as the methods that reported in the literature to illustrate the effectiveness and accuracy of the method. The results demonstrate that there is congruence between the numerical and the exact results to a high order of accuracy. Tables were generated to verify the accuracy convergence of the method and error. Figures are presented to show the excellent agreement between the results of this study and the results from literature. |
| format | Article |
| id | doaj-art-a8c1dd3a0aab41d08c948959eff58185 |
| institution | Kabale University |
| issn | 1687-0409 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-a8c1dd3a0aab41d08c948959eff581852025-02-03T07:24:16ZengWileyAbstract and Applied Analysis1687-04092022-01-01202210.1155/2022/2217882Approximation Technique for Solving Linear Volterra Integro-Differential Equations with Boundary ConditionsMohamed E. A. Alnair0Ahmed A. Khidir1Department of MathematicsDepartment of MathematicsThis paper presents a new technique for solving linear Volterra integro-differential equations with boundary conditions. The method is based on the blending of the Chebyshev spectral methods. The application of the proposed method leads the Volterra integro-differential equation to a system of algebraic equations that are easy to solve. Some examples are introduced and the obtained results are compared with exact solution as well as the methods that reported in the literature to illustrate the effectiveness and accuracy of the method. The results demonstrate that there is congruence between the numerical and the exact results to a high order of accuracy. Tables were generated to verify the accuracy convergence of the method and error. Figures are presented to show the excellent agreement between the results of this study and the results from literature.http://dx.doi.org/10.1155/2022/2217882 |
| spellingShingle | Mohamed E. A. Alnair Ahmed A. Khidir Approximation Technique for Solving Linear Volterra Integro-Differential Equations with Boundary Conditions Abstract and Applied Analysis |
| title | Approximation Technique for Solving Linear Volterra Integro-Differential Equations with Boundary Conditions |
| title_full | Approximation Technique for Solving Linear Volterra Integro-Differential Equations with Boundary Conditions |
| title_fullStr | Approximation Technique for Solving Linear Volterra Integro-Differential Equations with Boundary Conditions |
| title_full_unstemmed | Approximation Technique for Solving Linear Volterra Integro-Differential Equations with Boundary Conditions |
| title_short | Approximation Technique for Solving Linear Volterra Integro-Differential Equations with Boundary Conditions |
| title_sort | approximation technique for solving linear volterra integro differential equations with boundary conditions |
| url | http://dx.doi.org/10.1155/2022/2217882 |
| work_keys_str_mv | AT mohamedeaalnair approximationtechniqueforsolvinglinearvolterraintegrodifferentialequationswithboundaryconditions AT ahmedakhidir approximationtechniqueforsolvinglinearvolterraintegrodifferentialequationswithboundaryconditions |