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

Author

Listed:
  • Hoda S. Ali

    (Department of Mathematics, Faculty of Science, University of Tabuk, P.O. Box 741, Tabuk 71491, Saudi Arabia)

  • Elham Alali

    (Department of Mathematics, Faculty of Science, University of Tabuk, P.O. Box 741, Tabuk 71491, Saudi Arabia)

  • Abdelhalim Ebaid

    (Department of Mathematics, Faculty of Science, University of Tabuk, P.O. Box 741, Tabuk 71491, Saudi Arabia)

  • Fahad M. Alharbi

    (Department of Mathematics, Faculty of Science, University of Tabuk, P.O. Box 741, Tabuk 71491, Saudi Arabia)

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.

Suggested Citation

  • Hoda S. Ali & Elham Alali & Abdelhalim Ebaid & Fahad M. Alharbi, 2019. "Analytic Solution of a Class of Singular Second-Order Boundary Value Problems with Applications," Mathematics, MDPI, vol. 7(2), pages 1-10, February.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:2:p:172-:d:205941
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    References listed on IDEAS

    as
    1. Emad H. Aly & Abdelhalim Ebaid, 2013. "Exact Analytical Solution for Suction and Injection Flow with Thermal Enhancement of Five Nanofluids over an Isothermal Stretching Sheet with Effect of the Slip Model: A Comparative Study," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-14, October.
    2. Abdelhalim Ebaid & S. M. Khaled, 2014. "An Exact Solution for a Boundary Value Problem with Application in Fluid Mechanics and Comparison with the Regular Perturbation Solution," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-7, April.
    3. Abdelhalim Ebaid & Fahd Al Mutairi & S. M. Khaled, 2014. "Effect of Velocity Slip Boundary Condition on the Flow and Heat Transfer of Cu-Water and TiO 2 -Water Nanofluids in the Presence of a Magnetic Field," Advances in Mathematical Physics, Hindawi, vol. 2014, pages 1-9, August.
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    Cited by:

    1. Reem Alrebdi & Hind K. Al-Jeaid, 2023. "Accurate Solution for the Pantograph Delay Differential Equation via Laplace Transform," Mathematics, MDPI, vol. 11(9), pages 1-15, April.

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