Approximate solution for the Cauchy type singular integral equation using ODE approaches
The unknown function in the Cauchy type singular integral equation is expanded using Taylor expansion at the singular point t = x. Each term in the equation is then integrated yielding a linear ordinary differential equation. It is shown that the obtained linear ODE is uniformly convergent to the Ca...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Centre for Environment, Social and Economic Research Publications
2010
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| Online Access: | http://psasir.upm.edu.my/id/eprint/13252/ http://psasir.upm.edu.my/id/eprint/13252/1/Approximate%20solution%20for%20the%20Cauchy%20type%20singular%20integral%20equation%20using%20ODE%20approaches.pdf |
| _version_ | 1848842062076575744 |
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| author | Yaghobifar, Mohammad Nik Long, Nik Mohd Asri Eshkuratov, Zainidin K. Abdul Majid, Zanariah |
| author_facet | Yaghobifar, Mohammad Nik Long, Nik Mohd Asri Eshkuratov, Zainidin K. Abdul Majid, Zanariah |
| author_sort | Yaghobifar, Mohammad |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | The unknown function in the Cauchy type singular integral equation is expanded using Taylor expansion at the singular point t = x. Each term in the equation is then integrated yielding a linear ordinary differential equation. It is shown that the obtained linear ODE is uniformly convergent to the Cauchy type singular integral equation. The linear nth order ODE is reduced to a system of first order ODE which is solved numerically using Euler method. Numerical examples are presented to show the accuracy and efficiency of the method. |
| first_indexed | 2025-11-15T07:53:09Z |
| format | Article |
| id | upm-13252 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T07:53:09Z |
| publishDate | 2010 |
| publisher | Centre for Environment, Social and Economic Research Publications |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-132522019-10-31T03:31:57Z http://psasir.upm.edu.my/id/eprint/13252/ Approximate solution for the Cauchy type singular integral equation using ODE approaches Yaghobifar, Mohammad Nik Long, Nik Mohd Asri Eshkuratov, Zainidin K. Abdul Majid, Zanariah The unknown function in the Cauchy type singular integral equation is expanded using Taylor expansion at the singular point t = x. Each term in the equation is then integrated yielding a linear ordinary differential equation. It is shown that the obtained linear ODE is uniformly convergent to the Cauchy type singular integral equation. The linear nth order ODE is reduced to a system of first order ODE which is solved numerically using Euler method. Numerical examples are presented to show the accuracy and efficiency of the method. Centre for Environment, Social and Economic Research Publications 2010-03 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/13252/1/Approximate%20solution%20for%20the%20Cauchy%20type%20singular%20integral%20equation%20using%20ODE%20approaches.pdf Yaghobifar, Mohammad and Nik Long, Nik Mohd Asri and Eshkuratov, Zainidin K. and Abdul Majid, Zanariah (2010) Approximate solution for the Cauchy type singular integral equation using ODE approaches. International Journal of Mathematics and Computations, 6 (M10). pp. 7-13. ISSN 0974-5718; ESSN: 0974-570X http://www.ceser.in/ceserp/index.php/ijmc/article/view/2441 |
| spellingShingle | Yaghobifar, Mohammad Nik Long, Nik Mohd Asri Eshkuratov, Zainidin K. Abdul Majid, Zanariah Approximate solution for the Cauchy type singular integral equation using ODE approaches |
| title | Approximate solution for the Cauchy type singular integral equation using ODE approaches |
| title_full | Approximate solution for the Cauchy type singular integral equation using ODE approaches |
| title_fullStr | Approximate solution for the Cauchy type singular integral equation using ODE approaches |
| title_full_unstemmed | Approximate solution for the Cauchy type singular integral equation using ODE approaches |
| title_short | Approximate solution for the Cauchy type singular integral equation using ODE approaches |
| title_sort | approximate solution for the cauchy type singular integral equation using ode approaches |
| url | http://psasir.upm.edu.my/id/eprint/13252/ http://psasir.upm.edu.my/id/eprint/13252/ http://psasir.upm.edu.my/id/eprint/13252/1/Approximate%20solution%20for%20the%20Cauchy%20type%20singular%20integral%20equation%20using%20ODE%20approaches.pdf |