Fuzzy Volterra Integral Equations with Piecewise Continuous Kernels: Theory and Numerical Solution
This research focuses on addressing both linear and nonlinear fuzzy Volterra integral equations that feature piecewise continuous kernels. The problem is tackled using the method of successive approximations. The study discusses the existence and uniqueness of solutions for these fuzzy Volterra inte...
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| Format: | Article |
| Language: | English |
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Irkutsk State University
2024-12-01
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| Series: | Известия Иркутского государственного университета: Серия "Математика" |
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| Online Access: | https://mathizv.isu.ru/en/article/file?id=1508 |
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| author | S. Noeiaghdam D.N. Sidorov A.I. Dreglya |
| author_facet | S. Noeiaghdam D.N. Sidorov A.I. Dreglya |
| author_sort | S. Noeiaghdam |
| collection | DOAJ |
| description | This research focuses on addressing both linear and nonlinear fuzzy Volterra integral equations that feature piecewise continuous kernels. The problem is tackled using the method of successive approximations. The study discusses the existence and uniqueness of solutions for these fuzzy Volterra integral equations with piecewise kernels. Numerical results are obtained by applying the successive approximations method to examples for both linear and nonlinear scenarios. Error analysis graphs are plotted to illustrate the accuracy of the method. Furthermore, a comparative analysis is presented through graphs of approximate solutions for different fuzzy parameter values. To highlight the effectiveness and significance of the successive approximations method, a comparison is made with the traditional homotopy analysis technique. The results indicate that the successive approximation method outperforms the homotopy analysis method in terms of accuracy and effectiveness. |
| format | Article |
| id | doaj-art-cbd7dbbc595b47889bdfe57c669cb73e |
| institution | OA Journals |
| issn | 1997-7670 2541-8785 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | Irkutsk State University |
| record_format | Article |
| series | Известия Иркутского государственного университета: Серия "Математика" |
| spelling | doaj-art-cbd7dbbc595b47889bdfe57c669cb73e2025-08-20T02:21:06ZengIrkutsk State UniversityИзвестия Иркутского государственного университета: Серия "Математика"1997-76702541-87852024-12-015013650https://doi.org/10.26516/1997-7670.2024.50.36Fuzzy Volterra Integral Equations with Piecewise Continuous Kernels: Theory and Numerical SolutionS. NoeiaghdamD.N. SidorovA.I. DreglyaThis research focuses on addressing both linear and nonlinear fuzzy Volterra integral equations that feature piecewise continuous kernels. The problem is tackled using the method of successive approximations. The study discusses the existence and uniqueness of solutions for these fuzzy Volterra integral equations with piecewise kernels. Numerical results are obtained by applying the successive approximations method to examples for both linear and nonlinear scenarios. Error analysis graphs are plotted to illustrate the accuracy of the method. Furthermore, a comparative analysis is presented through graphs of approximate solutions for different fuzzy parameter values. To highlight the effectiveness and significance of the successive approximations method, a comparison is made with the traditional homotopy analysis technique. The results indicate that the successive approximation method outperforms the homotopy analysis method in terms of accuracy and effectiveness.https://mathizv.isu.ru/en/article/file?id=1508fuzzy volterra integral equationpiecewise kernelsuccessive approximationerror estimation |
| spellingShingle | S. Noeiaghdam D.N. Sidorov A.I. Dreglya Fuzzy Volterra Integral Equations with Piecewise Continuous Kernels: Theory and Numerical Solution Известия Иркутского государственного университета: Серия "Математика" fuzzy volterra integral equation piecewise kernel successive approximation error estimation |
| title | Fuzzy Volterra Integral Equations with Piecewise Continuous Kernels: Theory and Numerical Solution |
| title_full | Fuzzy Volterra Integral Equations with Piecewise Continuous Kernels: Theory and Numerical Solution |
| title_fullStr | Fuzzy Volterra Integral Equations with Piecewise Continuous Kernels: Theory and Numerical Solution |
| title_full_unstemmed | Fuzzy Volterra Integral Equations with Piecewise Continuous Kernels: Theory and Numerical Solution |
| title_short | Fuzzy Volterra Integral Equations with Piecewise Continuous Kernels: Theory and Numerical Solution |
| title_sort | fuzzy volterra integral equations with piecewise continuous kernels theory and numerical solution |
| topic | fuzzy volterra integral equation piecewise kernel successive approximation error estimation |
| url | https://mathizv.isu.ru/en/article/file?id=1508 |
| work_keys_str_mv | AT snoeiaghdam fuzzyvolterraintegralequationswithpiecewisecontinuouskernelstheoryandnumericalsolution AT dnsidorov fuzzyvolterraintegralequationswithpiecewisecontinuouskernelstheoryandnumericalsolution AT aidreglya fuzzyvolterraintegralequationswithpiecewisecontinuouskernelstheoryandnumericalsolution |