- About this Journal
- Abstracting and Indexing
- Aims and Scope
- 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
- Submit a Manuscript
- Table of Contents
ISRN Mathematical Physics
Volume 2013 (2013), Article ID 507145, 9 pages
Numerical Solution of Singular Lane-Emden Equation
Department of Applied Mathematics, School of Mathematical Sciences, University of Guilan, P.O. Box 1914, Rasht 41938, Iran
Received 24 June 2013; Accepted 13 July 2013
Academic Editors: N. E. Grandi and R. Schiappa
Copyright © 2013 Hossein Aminikhah and Sakineh Moradian. 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, An Introduction to the Study of Stellar Structure, Dover Publications, New York, NY, USA, 1967.
- O. U. Richardson, The Emission of Electricity From Hot Bodies, Longmans Green and Company, London, UK, 1921.
- C. M. Bender, K. A. Milton, S. S. Pinsky, and L. M. Simmons, Jr., “A new perturbative approach to nonlinear problems,” Journal of Mathematical Physics, vol. 30, no. 7, pp. 1447–1455, 1989.
- M. El-Gebeily and D. O’Regan, “A quasilinearization method for a class of second order singular nonlinear differential equations with nonlinear boundary conditions,” Nonlinear Analysis: Real World Applications, vol. 8, pp. 174–186, 2007.
- N. T. Shawagfeh, “Non-perturbative approximate solution for Lane-Emden equation,” Journal of Mathematical Physics, vol. 34, no. 9, pp. 4364–4369, 1993.
- A.-M. 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.-M. Wazwaz, “A new method for solving singular initial value problems in the second-order ordinary differential equations,” Applied Mathematics and Computation, vol. 128, no. 1, pp. 45–57, 2002.
- M. I. Nouh, “Accelerated power series solution of polytropic and isothermal gas spheres,” New Astronomy, vol. 9, no. 6, pp. 467–473, 2004.
- V. B. Mandelzweig and F. Tabakin, “Quasilinearization approach to nonlinear problems in physics with application to nonlinear ODEs,” Computer Physics Communications, vol. 141, no. 2, pp. 268–281, 2001.
- J. I. Ramos, “Linearization methods in classical and quantum mechanics,” Computer Physics Communications, vol. 153, no. 2, pp. 199–208, 2003.
- Y. Bozhkov and A. C. Gilli Martins, “Lie point symmetries and exact solutions of quasilinear differential equations with critical exponents,” Nonlinear Analysis: Theory, Methods & Applications, vol. 57, no. 5-6, pp. 773–793, 2004.
- E. Momoniat and C. Harley, “Approximate implicit solution of a Lane-Emden equation,” New Astronomy, vol. 11, pp. 520–526, 2006.
- H. Goenner and P. Havas, “Exact solutions of the generalized Lane-Emden equation,” Journal of Mathematical Physics, vol. 41, no. 10, pp. 7029–7042, 2000.
- S. Liao, “A new analytic algorithm of Lane-Emden type equations,” Applied Mathematics and Computation, vol. 142, no. 1, pp. 1–16, 2003.
- J.-H. He, “Variational approach to the Lane-Emden equation,” Applied Mathematics and Computation, vol. 143, no. 2-3, pp. 539–541, 2003.
- J. I. Ramos, “Series approach to the Lane-Emden equation and comparison with the homotopy perturbation method,” Chaos, Solitons and Fractals, vol. 38, no. 2, pp. 400–408, 2008.
- T. Özis and A. Yildirim, “Solutions of singular IVP’s of Lane-Emden type by homotopy pertutbation method,” Physics Letters A, vol. 369, pp. 70–76, 2007.
- T. Özis and A. Yildirim, “Solutions of singular IVPs of Lane-Emden type by the variational iteration method,” Nonlinear Analysis: Theory, Methods & Applications, vol. 70, no. 6, pp. 2480–2484, 2009.
- K. Parand and M. Razzaghi, “Rational Chebyshev tau method for solving higher-order ordinary differential equations,” International Journal of Computer Mathematics, vol. 81, no. 1, pp. 73–80, 2004.
- K. Parand and M. Razzaghi, “Rational Legendre approximation for solving some physical problems on semi-infinite intervals,” Physica Scripta, vol. 69, pp. 353–357, 2004.
- K. Parand, M. Shahini, and M. Dehghan, “Rational Legendre pseudospectral approach for solving nonlinear differential equations of Lane-Emden type,” Journal of Computational Physics, vol. 228, no. 23, pp. 8830–8840, 2009.
- 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.
- M. Razzaghi and S. Yousefi, “The Legendre wavelets operational matrix of integration,” International Journal of Systems Science, vol. 32, no. 4, pp. 495–502, 2001.