- 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
Abstract and Applied Analysis
Volume 2013 (2013), Article ID 378593, 10 pages
A Representation of the Exact Solution of Generalized Lane-Emden Equations Using a New Analytical Method
1Department of Mathematics, Faculty of Science, Al Balqa Applied University, Salt 19117, Jordan
2School of Mathematical Sciences, Universiti Kebangsaan Malaysia, 43600 Bangi, Selangor, Malaysia
Received 10 April 2013; Accepted 31 May 2013
Academic Editor: Massimo Furi
Copyright © 2013 Omar Abu Arqub 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. Iqbal and A. Javed, “Application of optimal homotopy asymptotic method for the analytic solution of singular Lane-Emden type equation,” Applied Mathematics and Computation, vol. 217, no. 19, pp. 7753–7761, 2011.
- K. Parand, M. Dehghan, A. R. Rezaei, and S. M. Ghaderi, “An approximation algorithm for the solution of the nonlinear Lane-Emden type equations arising in astrophysics using Hermite functions collocation method,” Computer Physics Communications, vol. 181, no. 6, pp. 1096–1108, 2010.
- A. Wazwaz, “A new algorithm for solving differential equations of Lane-Emden type,” Applied Mathematics and Computation, vol. 118, no. 2-3, pp. 287–310, 2001.
- A. Yildirim and T. Ozi, “Solutions of singular IVPs of Lane-Emden type by homotopy perturbation method,” Physics Letters A, vol. 369, no. 1-2, pp. 70–76, 2007.
- C. Hunter, “Series solutions for polytropes and the isothermal sphere,” Monthly Notices of the Royal Astronomical Society, vol. 328, no. 3, pp. 839–847, 2001.
- M. I. Nouh, “Accelerated power series solution of polytropic and isothermal gas spheres,” New Astronomy, vol. 9, no. 6, pp. 467–473, 2004.
- B. M. Mirza, “Approximate analytical solutions of the Lane-Emden equation for a self-gravitating isothermal gas sphere,” Monthly Notices of the Royal Astronomical Society, vol. 395, no. 4, pp. 2288–2291, 2009.
- K. Boubaker and R. A. Van Gorder, “Application of the BPES to Lane-Emden equations governing polytropic and isothermal gas spheres,” New Astronomy, vol. 17, no. 6, pp. 565–569, 2012.
- S. Chandrasekhar, Introduction to the Study of Stellar Structure, Dover Publications, New York, NY, USA, 1967.
- H. T. Davis, Introduction to Nonlinear Differential and Integral Equations, Dover Publications, New York, NY, USA, 1962.
- O. U. Richardson, The Emission of Electricity of Hot Bodies, London, UK, Longmans Green and Company edition, 1921.
- P. L. Chambré, “On the solution of the poisson-boltzmann equation with application to the theory of thermal explosions,” The Journal of Chemical Physics, vol. 20, no. 11, pp. 1795–1797, 1952.
- M. Dehghan and F. Shakeri, “Approximate solution of a differential equation arising in astrophysics using the variational iteration method,” New Astronomy, vol. 13, no. 1, pp. 53–59, 2008.
- J. H. Lane, “On theoretical temperature of the sun under the hypothesis of a gaseous mass maintaining its internal heat and depending on the laws of gases known to terrestrial experiment,” The American Journal of Science and Arts, vol. 2, pp. 57–74, 1870.
- R. Emden, Gaskugeln, Teubner, Berlin, Germany, 1907.
- N. T. Shawagfeh, “Nonperturbative approximate solution for Lane-Emden equation,” Journal of Mathematical Physics, vol. 34, no. 9, pp. 4364–4369, 1993.
- G. Adomian, R. Rach, and N. T. Shawagfeh, “On the analytic solution of the lane-emden equation,” Foundations of Physics Letters, vol. 8, no. 2, pp. 161–181, 1995.
- O. Abu Arqub, “Series solution of fuzzy differential equations under strongly generalized differentiability,” Journal of Advanced Research in Applied Mathematics, vol. 5, no. 1, p. 31, 2013.
- S. Yuzbasi and M. Sezer, “An improved Bessel collocation method with a residual error function to solve a class of Lane-Emden differential equations,” Mathematical and Computer Modelling, vol. 57, no. 5-6, pp. 1298–1311, 2012.
- A. El-Ajou, O. Abu Arqub, and S. Momani, “Homotopy analysis method for second-order boundary value problems of integrodifferential equations,” Discrete Dynamics in Nature and Society, vol. 2012, Article ID 365792, 18 pages, 2012.
- O. Abu Arqub, M. Al-Smadi, and S. Momani, “Application of reproducing kernel method for solving nonlinear Fredholm-Volterra integrodifferential equations,” Abstract and Applied Analysis, vol. 2012, Article ID 839836, 16 pages, 2012.
- M. Al-Smadi, O. Abu Arqub, and S. Momani, “A computational method for two point boundary value problems of fourth-order mixed integrodifferential equations,” Mathematical Problems in Engineering, vol. 2013, Article ID 832074, 10 pages, 2013.
- O. Abu Arqub and A. El-Ajou, “Solution of the fractional epidemic model by homotopy analysis method,” Journal of King Saud University, vol. 25, no. 1, pp. 73–81, 2013.
- O. Abu Arqub, A. El-Ajou, S. Momani, and N. Shawagfeh, “Analytical solutions of fuzzy initial value problems by HAM,” Applied Mathematics and Information Sciences. In press.
- O. Abu Arqub, M. Al-Smadi, and N. Shawagfeh, “Solving Fredholm integro-differential equations using reproducing kernel Hilbert space method,” Applied Mathematics and Computation, vol. 219, no. 17, pp. 8938–8948, 2013.
- O. Abu 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.
- R. V. Dukkipati, Numerical Methods, New Age International, New Delhi, India, 2010.
- W. B. Bonnor, “Boyle's law and gravitational instability,” Monthly Notices of the Royal Astronomical Society, vol. 116, pp. 351–359, 1956.
- R. Ebert, “Uber die Verdichtung von H I-Gebieten,” Zeitschrift Fur Astrophysik, vol. 37, pp. 217–232, 1955.
- R. A. van Gorder, “Exact first integrals for a Lane-Emden equation of the second kind modeling a thermal explosion in a rectangular slab,” New Astronomy, vol. 16, no. 8, pp. 492–497, 2011.
- R. A. van Gorder, “Analytical solutions to a quasilinear differential equation related to the Lane-Emden equation of the second kind,” Celestial Mechanics and Dynamical Astronomy, vol. 109, no. 2, pp. 137–145, 2011.
- R. A. van Gorder, “An elegant perturbation solution for the Lane-Emden equation of the second kind,” New Astronomy, vol. 16, no. 2, pp. 65–67, 2011.
- C. Harley and E. Momoniat, “First integrals and bifurcations of a Lane-Emden equation of the second kind,” Journal of Mathematical Analysis and Applications, vol. 344, no. 2, pp. 757–764, 2008.