- About this Journal ·
- Abstracting and Indexing ·
- Advance Access ·
- Aims and Scope ·
- Annual Issues ·
- Article Processing Charges ·
- Articles in Press ·
- Author Guidelines ·
- Bibliographic Information ·
- Citations to this Journal ·
- Contact Information ·
- Editorial Board ·
- Editorial Workflow ·
- Free eTOC Alerts ·
- Publication Ethics ·
- Reviewers Acknowledgment ·
- Submit a Manuscript ·
- Subscription Information ·
- Table of Contents
Journal of Applied Mathematics
Volume 2013 (2013), Article ID 468909, 8 pages
Numerical Scheme for Solving Singular Two-Point Boundary Value Problems
1School of Mathematical Sciences, Universiti Kebangsaan Malaysia, 43600 Bangi, Selangor, Malaysia
2Department of Mathematics, Faculty of Science, Hashemite University, 13115 Zarqa, Jordan
Received 25 December 2012; Revised 5 March 2013; Accepted 11 March 2013
Academic Editor: Saeid Abbasbandy
Copyright © 2013 N. Ratib Anakira et al. 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.
- S. Chandrasekhar, Hydrodynamic and Hydromagnetic Stability, Dover, New York, NY, USA, 1981.
- A. S. Bataineh, M. S. M. Noorani, and I. Hashim, “Approximate solutions of singular two-point BVPs by modified homotopy analysis method,” Physics Letters A, vol. 372, no. 22, pp. 4062–4066, 2008.
- J. Lu, “Variational iteration method for solving two-point boundary value problems,” Journal of Computational and Applied Mathematics, vol. 207, no. 1, pp. 92–95, 2007.
- A. S. V. R. Kanth and Y. N. Reddy, “Cubic spline for a class of singular two-point boundary value problems,” Applied Mathematics and Computation, vol. 170, no. 2, pp. 733–740, 2005.
- A. S. V. R. Kanth and K. Aruna, “Solution of singular two-point boundary value problems using differential transformation method,” Physics Letters A, vol. 372, no. 26, pp. 4671–4673, 2008.
- A. Ebaid and M. D. Aljoufi, “Exact solutions for a class of singular two-point boundary value problems using Adomian decomposition method,” Applied Mathematical Sciences, vol. 6, no. 121–124, pp. 6097–6108, 2012.
- O. A. Arqub, Z. Abo-Hammour, S. Momani, and N. Shawagfeh, “Solving singular two-point boundary value problems using continuous genetic algorithm,” Abstract and Applied Analysis, vol. 2012, Article ID 205391, 25 pages, 2012.
- K. Al-Khaled, “Theory and computation in singular boundary value problems,” Chaos, Solitons and Fractals, vol. 33, no. 2, pp. 678–684, 2007.
- M. Jalaal, D. D. Ganji, and G. Ahmadi, “Analytical investigation on acceleration motion of a vertically falling spherical particle in incompressible Newtonian media,” Advanced Powder Technology, vol. 21, no. 3, pp. 298–304, 2010.
- M. Jalaal and D. D. Ganji, “An analytical study on motion of a sphere rolling down an inclined plane submerged in a Newtonian fluid,” Powder Technology, vol. 198, no. 1, pp. 82–92, 2010.
- M. Jalaal and D. D. Ganji, “On unsteady rolling motion of spheres in inclined tubes filled with incompressible Newtonian fluids,” Advanced Powder Technology, vol. 22, no. 1, pp. 58–67, 2011.
- M. Jalaal, M. G. Nejad, P. Jalili et al., “Homotopy perturbation method for motion of a spherical solid particle in plane couette fluid flow,” Computers and Mathematics with Applications, vol. 61, no. 8, pp. 2267–2270, 2011.
- M. Esmaeilpour and D. D. Ganji, “Application of He's homotopy perturbation method to boundary layer flow and convection heat transfer over a flat plate,” Physics Letters A, vol. 372, no. 1, pp. 33–38, 2007.
- S. J. Liao, The proposed homotopy analysis techniques for the solution of nonlinear problems [Ph.D. thesis], Shanghai Jiao Tong University, 1992.
- S. J. Liao, Beyond Perturbation: Introduction to the Homotopy Analysis Method, vol. 2 of CRC Series: Modern Mechanics and Mathematics, Chapman & Hall/CRC, Boca Raton, Fla, USA, 2004.
- S. J. Liao, “An explicit, totally analytic approximate solution for Blasius' viscous flow problems,” International Journal of Non-Linear Mechanics, vol. 34, no. 4, pp. 759–778, 1999.
- S. J. Liao, “On the homotopy analysis method for nonlinear problems,” Applied Mathematics and Computation, vol. 147, no. 2, pp. 499–513, 2004.
- S. J. Liao, “An approximate solution technique not depending on small parameters: a special example,” International Journal of Non-Linear Mechanics, vol. 30, no. 3, pp. 371–380, 1995.
- S. J. Liao, “A kind of approximate solution technique which does not depend upon small parameters—II: an application in fluid mechanics,” International Journal of Non-Linear Mechanics, vol. 32, no. 5, pp. 815–822, 1997.
- S. J. Liao, “Comparison between the homotopy analysis method and homotopy perturbation method,” Applied Mathematics and Computation, vol. 169, no. 2, pp. 1186–1194, 2005.
- S. J. Liao, “A new branch of solutions of boundary-layer flows over an impermeable stretched plate,” International Journal of Heat and Mass Transfer, vol. 48, no. 12, pp. 2529–2539, 2005.
- T. Hayat and M. Khan, “Homotopy solutions for a generalized second-grade fluid past a porous plate,” Nonlinear Dynamics, vol. 42, no. 4, pp. 395–405, 2005.
- M. Ayub, A. Rasheed, and T. Hayat, “Exact flow of a third grade fluid past a porous plate using homotopy analysis method,” International Journal of Engineering Science, vol. 41, no. 18, pp. 2091–2103, 2003.
- I. T. Abu-Zaid and M. A. El-Gebeily, “A finite difference method for approximating the solution of a certain class of singular two-point boundary value problems,” Arab Journal of Mathematical Sciences, vol. 1, no. 1, pp. 25–39, 1995.
- A. M. Siddiqui, M. Ahmed, and Q. K. Ghori, “Couette and poiseuille flows for non-newtonian fluids,” International Journal of Nonlinear Sciences and Numerical Simulation, vol. 7, no. 1, pp. 15–26, 2006.
- N. Herisanu, V. Marinca, T. Dordea, and G. Madescu, “A new analytical approach to nonlinear vibration of an electric machine,” Proceedings of Romanian Academy A, vol. 9, no. 3, 2008.
- V. Marinca, N. Herisanu, C. Bota, and B. Marinca, “An optimal homotopy asymptotic method applied to the steady flow of a fourth-grade fluid past a porous plate,” Applied Mathematics Letters, vol. 22, no. 2, pp. 245–251, 2009.
- V. Marinca, N. Herisanu, and I. Nemes, “Optimal homotopy asymptotic method with application to thin film flow,” Central European Journal of Physics, vol. 6, no. 3, pp. 648–653, 2008.
- V. Marinca and N. Herisanu, “Application of optimal homotopy asymptotic method for solving nonlinear equations arising in heat transfer,” International Communications in Heat and Mass Transfer, vol. 35, no. 6, pp. 710–715, 2008.
- J. Ali, S. Islam, S. Islam, and G. Zaman, “The solution of multipoint boundary value problems by the optimal homotopy asymptotic method,” Computers & Mathematics with Applications, vol. 59, no. 6, pp. 2000–2006, 2010.
- M. Cui and F. Geng, “Solving singular two-point boundary value problem in reproducing kernel space,” Journal of Computational and Applied Mathematics, vol. 205, no. 1, pp. 6–15, 2007.