Analytical-approximate solution of Abel integral equations
It is known that Abel integral equation has a solution in a closed form, with a removable singularity.The presence of Volterra integrals with weak singularity is not always integrable for continuous differentiable class of functions.In this work we propose an analytical approximate method for the so...
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| Format: | Article |
| Language: | English |
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Hikari
2011
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| Online Access: | http://psasir.upm.edu.my/id/eprint/13105/ http://psasir.upm.edu.my/id/eprint/13105/1/Analytical-approximate%20solution%20of%20Abel%20integral%20equations.pdf |
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| author | Yaghobifar, Mohammad Nik Long, Nik Mohd Asri Eshkuratov, Zainidin K. |
| author_facet | Yaghobifar, Mohammad Nik Long, Nik Mohd Asri Eshkuratov, Zainidin K. |
| author_sort | Yaghobifar, Mohammad |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | It is known that Abel integral equation has a solution in a closed form, with a removable singularity.The presence of Volterra integrals with weak singularity is not always integrable for continuous differentiable class of functions.In this work we propose an analytical approximate method for the solution of Abel integral equations.
We showed that the proposed method is exact for the known function in the cases of polynomials and irrational function of the form f(t)tα+1(a0+a1t+···+antn),0<α<1.For the derivation of the proposed method we expand the known function to the Taylor series around a singular points. Substituting this expansion into the solution of Abel equation we could remove the singularity. All evaluations of the integrals are calculated analytically. The obtained solution is a series that is uniformly convergence to the exact solution. |
| first_indexed | 2025-11-15T07:52:30Z |
| format | Article |
| id | upm-13105 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T07:52:30Z |
| publishDate | 2011 |
| publisher | Hikari |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-131052019-10-31T03:27:59Z http://psasir.upm.edu.my/id/eprint/13105/ Analytical-approximate solution of Abel integral equations Yaghobifar, Mohammad Nik Long, Nik Mohd Asri Eshkuratov, Zainidin K. It is known that Abel integral equation has a solution in a closed form, with a removable singularity.The presence of Volterra integrals with weak singularity is not always integrable for continuous differentiable class of functions.In this work we propose an analytical approximate method for the solution of Abel integral equations. We showed that the proposed method is exact for the known function in the cases of polynomials and irrational function of the form f(t)tα+1(a0+a1t+···+antn),0<α<1.For the derivation of the proposed method we expand the known function to the Taylor series around a singular points. Substituting this expansion into the solution of Abel equation we could remove the singularity. All evaluations of the integrals are calculated analytically. The obtained solution is a series that is uniformly convergence to the exact solution. Hikari 2011 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/13105/1/Analytical-approximate%20solution%20of%20Abel%20integral%20equations.pdf Yaghobifar, Mohammad and Nik Long, Nik Mohd Asri and Eshkuratov, Zainidin K. (2011) Analytical-approximate solution of Abel integral equations. International Mathematical Forum, 6 (5). pp. 211-221. ISSN 1312-7594; ESSN: 1314-7536 http://www.m-hikari.com/imf-2011/5-8-2011/index.html |
| spellingShingle | Yaghobifar, Mohammad Nik Long, Nik Mohd Asri Eshkuratov, Zainidin K. Analytical-approximate solution of Abel integral equations |
| title | Analytical-approximate solution of Abel integral equations |
| title_full | Analytical-approximate solution of Abel integral equations |
| title_fullStr | Analytical-approximate solution of Abel integral equations |
| title_full_unstemmed | Analytical-approximate solution of Abel integral equations |
| title_short | Analytical-approximate solution of Abel integral equations |
| title_sort | analytical-approximate solution of abel integral equations |
| url | http://psasir.upm.edu.my/id/eprint/13105/ http://psasir.upm.edu.my/id/eprint/13105/ http://psasir.upm.edu.my/id/eprint/13105/1/Analytical-approximate%20solution%20of%20Abel%20integral%20equations.pdf |