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Linked References

1. S. Chandrasekhar, An Introduction to the Study of Stellar Structure, Dover, New York, NY, USA, 1958.
2. H. T. Davis, Introduction to Nonlinear Differential and Integral Equations, Dover, New York, NY, USA, 1962.
3. 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. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
4. A.-M. Wazwaz, “Adomian decomposition method for a reliable treatment of the Emden-Fowler equation,” Applied Mathematics and Computation, vol. 161, no. 2, pp. 543–560, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
5. V. S. Ertürk, “Differential transformation method for solving differential equations of Lane-Emden type,” Mathematical & Computational Applications, vol. 12, no. 3, pp. 135–139, 2007. View at Zentralblatt MATH
6. A. Yildirim and T. Öziş, “Solutions of singular IVPs of Lane-Emden type by homotopy perturbation method,” Physics Letters, Section A, vol. 369, no. 1-2, pp. 70–76, 2007. View at Publisher · View at Google Scholar · View at Scopus
7. A. S. Bataineh, M. S. M. Noorani, and I. Hashim, “Homotopy analysis method for singular IVPs of Emden-Fowler type,” Communications in Nonlinear Science and Numerical Simulation, vol. 14, no. 4, pp. 1121–1131, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
8. S. Liao, “A new analytic algorithm of Lane-Emden type equations,” Applied Mathematics and Computation, vol. 142, no. 1, pp. 1–16, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
9. A. Aslanov, “Determination of convergence intervals of the series solutions of Emden-Fowler equations using polytropes and isothermal spheres,” Physics Letters. A, vol. 372, no. 20, pp. 3555–3561, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
10. 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. View at Publisher · View at Google Scholar · View at Scopus
11. C. Mohan and A. R. Al-Bayaty, “Power-series solutions of the Lane-Emden equation,” Astrophysics and Space Science, vol. 73, no. 1, pp. 227–239, 1980. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
12. I. W. Roxburgh and L. M. Stockman, “Power series solutions of the polytrope equations,” Monthly Notices of the Royal Astronomical Society, vol. 303, no. 3, pp. 466–470, 1999. View at Publisher · View at Google Scholar · View at Scopus
13. Z. F. Seidov, “The power series as solution of the Lane-Emden equation with index two,” Doklady Akademii Nauk SSSR, vol. 35, pp. 21–24, 1979.
14. J. H. He, “Variational approach to the Lane-Emden equation,” Applied Mathematics and Computation, vol. 143, no. 2-3, pp. 539–541, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
15. A. Yıldırım and T. Öziş, “Solutions of singular IVPs of Lane-Emden type by the variational iteration method,” Nonlinear Analysis, vol. 70, no. 6, pp. 2480–2484, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
16. S. S. Motsa and S. Shateyi, “New analytic solution to the Lane-Emden equation of index 2,” Mathematical Problems in Engineering, vol. 2012, Article ID 614796, 19 pages, 2012. View at Publisher · View at Google Scholar
17. S. Liao, Beyond Perturbation: Introduction to Homotopy Analysis Method, vol. 2 of CRC Series: Modern Mechanics and Mathematics, Chapman & Hall/CRC, Boca Raton, Fla, USA, 2004.
18. K. Parand and M. Razzaghi, “Rational legendre approximation for solving some physical problems on semi-infinite intervals,” Physica Scripta, vol. 69, no. 5, pp. 353–357, 2004. View at Publisher · View at Google Scholar · View at Scopus
19. K. Parand and A. Pirkhedri, “Sinc-Collocation method for solving astrophysics equations,” New Astronomy, vol. 15, no. 6, pp. 533–537, 2010. View at Publisher · View at Google Scholar · View at Scopus
20. K. Parand, A. R. Rezaei, and A. Taghavi, “Lagrangian method for solving LaneEmden type equation arising in astrophysics on semi-infinite domains,” Acta Astronautica, vol. 67, no. 7-8, pp. 673–680, 2010. View at Publisher · View at Google Scholar · View at Scopus
21. S. S. Motsa and P. Sibanda, “A new algorithm for solving singular IVPs of Lane-Emden type,” in Proceedings of the 4th International Conference on Applied Mathematics, Simulation, Modelling (ASM'10), pp. 176–180, Corfu Island, Greece, July 2010. View at Scopus
22. K. Parand, S. Abbasbandy, S. Kazem, and A. R. Rezaei, “An improved numerical method for a class of astrophysics problems based on radial basis functions,” Physica Scripta, vol. 83, no. 1, Article ID 015011, 2011. View at Publisher · View at Google Scholar · View at Scopus
23. G. P. Horedt, “Seven-digit tables of Lane-Emden functions,” Astrophysics and Space Science, vol. 126, no. 2, pp. 357–408, 1986. View at Publisher · View at Google Scholar · View at Scopus
24. Z. F. Seidov, “Lane-Emden equation: perturbation method,” In press, http://arxiv.org/abs/astro-ph/0402130.
25. J. P. Boyd, “Chebyshev spectral methods and the Lane-Emden problem,” Numerical Mathematics. Theory, Methods and Applications, vol. 4, no. 2, pp. 142–157, 2011.
26. D. A. Frank-Kamenetskii, Diffusion and Heat Transfer in Chemical Kinetics, Plenum Press, New York, NY, USA, 1969.
27. M. Kubíček and V. Hlavačék, Numerical Solution of Nonlinear Boundary Value Problems with Applications, Prentice-Hall, Englewood Cliffs, NJ, USA, 1983.
28. S. A. Khuri and A. Sayfy, “A novel approach for the solution of a class of singular boundary value problems arising in physiology,” Mathematical and Computer Modelling, vol. 52, no. 3-4, pp. 626–636, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
29. M. Kumar and N. Singh, “Modified Adomian Decomposition Method and computer implementation for solving singular boundary value problems arising in various physical problems,” Computers and Chemical Engineering, vol. 34, no. 11, pp. 1750–1760, 2010. View at Publisher · View at Google Scholar · View at Scopus
30. 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. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
31. E. Momoniat and C. Harley, “Approximate implicit solution of a Lane-Emden equation,” New Astronomy, vol. 11, no. 7, pp. 520–526, 2006. View at Publisher · View at Google Scholar · View at Scopus
32. A. Asaithambi, “A shooting method for nonlinear heat transfer using automatic differentiation,” Applied Mathematics and Computation, vol. 180, no. 1, pp. 264–269, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
33. H. Çaǧlar, N. Çaǧlar, and M. Özer, “B-spline solution of non-linear singular boundary value problems arising in physiology,” Chaos, Solitons and Fractals, vol. 39, no. 3, pp. 1232–1237, 2009. View at Publisher · View at Google Scholar · View at Scopus
34. S. R. K. Iyengar and P. Jain, “Spline finite difference methods for singular two point boundary value problems,” Numerische Mathematik, vol. 50, no. 3, pp. 363–376, 1987. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
35. M. Kumar and Y. Gupta, “Methods for solving singular boundary value problems using splines: a review,” Journal of Applied Mathematics and Computing, vol. 32, no. 1, pp. 265–278, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
36. F. G. Awad, P. Sibanda, S. S. Motsa, and O. D. Makinde, “Convection from an inverted cone in a porous medium with cross-diffusion effects,” Computers & Mathematics with Applications, vol. 61, no. 5, pp. 1431–1441, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
37. Z. G. Makukula, P. Sibanda, and S. S. Motsa, “A novel numerical technique for two-dimensional laminar flow between two moving porous walls,” Mathematical Problems in Engineering, vol. 2010, Article ID 528956, 15 pages, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
38. S. S. Motsa and S. Shateyi, “A new approach for the solution of three-dimensional magnetohydrodynamic rotating flow over a shrinking sheet,” Mathematical Problems in Engineering, vol. 2010, Article ID 586340, 2010. View at Publisher · View at Google Scholar · View at Scopus
39. S. S. Motsa, “New algorithm for solving non-linear BVPs in heat transfer,” International Journal of Modeling, Simulation & Scientific Computing, vol. 2, no. 3, pp. 355–373, 2011. View at Publisher · View at Google Scholar
40. C. Canuto, M. Y. Hussaini, A. Quarteroni, and T. A. Zang, Spectral Methods in Fluid Dynamics, Springer Series in Computational Physics, Springer, New York, NY, USA, 1988.
41. L. N. Trefethen, Spectral Methods in MATLAB, vol. 10, SIAM, Philadelphia, Pa, USa, 2000. View at Publisher · View at Google Scholar
42. C. Harley and E. Momoniat, “Efficient boundary value problem solution for a Lane-Emden equation,” Mathematical & Computational Applications, vol. 15, no. 4, pp. 613–620, 2010.
43. G. P. Horedt, Polytropes Applications in Astrophysics and Related Fields, Kluwer Academic Publishers, Dordrecht, The Netherlands, 2004.