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Mathematics 2019, 7(2), 172; https://doi.org/10.3390/math7020172

Analytic Solution of a Class of Singular Second-Order Boundary Value Problems with Applications

Department of Mathematics, Faculty of Science, University of Tabuk, P.O. Box 741, Tabuk 71491, Saudi Arabia
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Received: 15 December 2018 / Revised: 31 January 2019 / Accepted: 3 February 2019 / Published: 14 February 2019
(This article belongs to the Section Engineering Mathematics)
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Abstract

Recently, it was observed that the concentration/heat transfer of pure/nano fluids are finally governed by singular second-order boundary value problems with exponential coefficients. These coefficients were transformed into polynomials and therefore the governing equations become singular in a new independent variable. Unfortunately, the published approximate solutions in the literature suffer from some weaknesses as showed by one of the present coauthors. Hence, the exact solution for such types of problems becomes a challenge. In this paper, a straightforward approach is presented to obtaining the exact solution for such class of singular second-order boundary value problems. The results are also applied to some selected problems within the literature. Accordingly, the published solutions are recovered as special cases of the present ones. View Full-Text
Keywords: ordinary differential equation; hypergeometric series; singular boundary value problem; Laplace transform; nanofluid ordinary differential equation; hypergeometric series; singular boundary value problem; Laplace transform; nanofluid
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Ali, H.S.; Alali, E.; Ebaid, A.; Alharbi, F.M. Analytic Solution of a Class of Singular Second-Order Boundary Value Problems with Applications. Mathematics 2019, 7, 172.

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