On a modified Bernstein operators approximation method for computational solution of Volterra integral equation
Abstract The main feature of this paper is an application of the modified Bernstein operator in the approximate and numerical solution of integral equations. The stability of the algorithm is discussed in the context of errors resulting from the numerical approximation of Volterra integral equations...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2025-01-01
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| Series: | Journal of Inequalities and Applications |
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| Online Access: | https://doi.org/10.1186/s13660-024-03225-y |
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| _version_ | 1832585318325288960 |
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| author | Khursheed J. Ansari Fuat Usta |
| author_facet | Khursheed J. Ansari Fuat Usta |
| author_sort | Khursheed J. Ansari |
| collection | DOAJ |
| description | Abstract The main feature of this paper is an application of the modified Bernstein operator in the approximate and numerical solution of integral equations. The stability of the algorithm is discussed in the context of errors resulting from the numerical approximation of Volterra integral equations. The mechanism of the proposed method is explained in detail, including its main features. Furthermore, a comparison with an alternative numerical technique is made, and the superiority of the proposed solution is shown. Numerical experiments are also performed to verify the validity of the proposed method and to assess its accuracy. Finally, several conclusions are drawn from the results of the numerical experiments. The proposed method provides a powerful and efficient tool for the approximate solution of Volterra integral equations, and its results are promising. The results obtained from this algorithm are useful in the numerical analysis of integral equations. |
| format | Article |
| id | doaj-art-d1fb8caa76f64a0892968b704e90e4fe |
| institution | Kabale University |
| issn | 1029-242X |
| language | English |
| publishDate | 2025-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Inequalities and Applications |
| spelling | doaj-art-d1fb8caa76f64a0892968b704e90e4fe2025-01-26T12:57:39ZengSpringerOpenJournal of Inequalities and Applications1029-242X2025-01-012025111510.1186/s13660-024-03225-yOn a modified Bernstein operators approximation method for computational solution of Volterra integral equationKhursheed J. Ansari0Fuat Usta1Department of Mathematics, College of Science, King Khalid UniversityDepartment of Mathematics, Faculty of Science and Arts, Düzce UniversityAbstract The main feature of this paper is an application of the modified Bernstein operator in the approximate and numerical solution of integral equations. The stability of the algorithm is discussed in the context of errors resulting from the numerical approximation of Volterra integral equations. The mechanism of the proposed method is explained in detail, including its main features. Furthermore, a comparison with an alternative numerical technique is made, and the superiority of the proposed solution is shown. Numerical experiments are also performed to verify the validity of the proposed method and to assess its accuracy. Finally, several conclusions are drawn from the results of the numerical experiments. The proposed method provides a powerful and efficient tool for the approximate solution of Volterra integral equations, and its results are promising. The results obtained from this algorithm are useful in the numerical analysis of integral equations.https://doi.org/10.1186/s13660-024-03225-yModified Bernstein’s approximation techniqueVolterra integral equation of the first and second kindNumerical schemeConvergence analysis |
| spellingShingle | Khursheed J. Ansari Fuat Usta On a modified Bernstein operators approximation method for computational solution of Volterra integral equation Journal of Inequalities and Applications Modified Bernstein’s approximation technique Volterra integral equation of the first and second kind Numerical scheme Convergence analysis |
| title | On a modified Bernstein operators approximation method for computational solution of Volterra integral equation |
| title_full | On a modified Bernstein operators approximation method for computational solution of Volterra integral equation |
| title_fullStr | On a modified Bernstein operators approximation method for computational solution of Volterra integral equation |
| title_full_unstemmed | On a modified Bernstein operators approximation method for computational solution of Volterra integral equation |
| title_short | On a modified Bernstein operators approximation method for computational solution of Volterra integral equation |
| title_sort | on a modified bernstein operators approximation method for computational solution of volterra integral equation |
| topic | Modified Bernstein’s approximation technique Volterra integral equation of the first and second kind Numerical scheme Convergence analysis |
| url | https://doi.org/10.1186/s13660-024-03225-y |
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