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Analytical-approximate solution of Abel integral equations


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


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.

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Additional Metadata

Item Type: Article
Divisions: Faculty of Science
Institute for Mathematical Research
Publisher: Hikari
Keywords: Abel integral equation; Weakly singular integral; Taylor expansion; Approximate solution
Depositing User: Nurul Ainie Mokhtar
Date Deposited: 07 Jun 2015 01:51
Last Modified: 31 Oct 2019 03:27
URI: http://psasir.upm.edu.my/id/eprint/13105
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