A new algorithm for solving singular IVPs of Lane-Emden type

International Conference on Applied Mathematics, Simulation, Modelling - Proceedings

Volumn , Issue , 2010, Pages 176-180

  Motsa, Sandile S ^a   Sibanda, Precious ^b  

^a UNIVERSITY OF SWAZILAND   (Swaziland)

^b UNIVERSITY OF KWAZULU NATAL   (South Africa)

Author keywords

Lane Emden equation; Linearization method; Series solution; Singular IVPs; Spectral method

Indexed keywords

LANE-EMDEN EQUATION; LINEARIZATION METHOD; SERIES SOLUTIONS; SINGULAR IVPS; SPECTRAL METHODS;

ALGORITHMS; ASTROPHYSICS; COMPUTATIONAL EFFICIENCY; INITIAL VALUE PROBLEMS; NONLINEAR EQUATIONS; NUMERICAL METHODS; SPECTROSCOPY;

MATHEMATICAL MODELS;

EID: 79958745512     PISSN: 17924332     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (35)

1. J. H. Lane, "On the theoretical temperature of the sun under the hypothesis of a gaseous mass maintaining its volume by its internal heat and depending on the laws of gases known to terrestrial experiment," The American Journal of Science and Arts, vol. 50, pp. 57-74, 1870.
2. R. Emden, Gaskugeln Anwendungen der Mechan. Warmtheorie, Druck und Verlag Von B. G. Teubner, Leipzig and Berlin, 1907.
3. J. M Dixon, J. A. Tuszyński, "Solutions of a generalized Emden equation and their physical significance," Phys Rev A, vol. 41, pp. 4166-4173, 1990.
4. E. Fermi, "Un metodo statistico per la determinazione di alcune priorieta dell'atome," Rend. Accad. Naz. Lincei, vol. 6, pp. 602-607, 1927.
5. R. H. Fowler, "The solutions of Emden's and similar differential equations," MNRAS, vol. 91, pp. 63-91, 1930.
6. D. A. Frank-Kamenetskii, Diffusion and heat exchange in chemical kinetics, Princeton University Press, Princeton, 1955.
7. S. Chandrasekhar, An introduction to the study of stellar structure, Dover, New York, 1939.
8. A. S. Eddington, The internal constitution of the stars, Cambridge University Press, London, 1926.
9. L. Spitzer, "The Dynamics of the Interstellar Medium," Ap.J., vol. 95, pp. 329-344, 1942.
10. Z. F. Seidov, J. P. Sharma, "Lane-Emden equation of index 5 and Padé appromations," Cellular and Molecular Life Sciences, vol. 35, pp. 293-294, 1979.
11. J. P. Sharma, "On some transformations of the generalized isothermal equationss and Padeé approximants," Indian J. Pure Appl. Math, vol. 12, pp. 119-128, 1981.
12. M. I. Nouh, "Accelerated power-series solution of polytropic and isothermal gas spheres," New Astronomy, vol. 9, pp. 467-473, 2004.
13. J. I. Ramos, "Series approach to Lane-Emden equation and comparison with the homotopy perturbation method," Chaos Soliton and Fract., vol. 38, pp. 400-408, 2008. (Pubitemid 351627012)
14. Z. F. Seidov, R. Kh. Kuzakhmedov, "New solutions of the Lane-Emden equation," Soviet Astronomy, vol. 22, pp. 711-714, 1977.
15. C. Mohan, A. R. Al-Bayaty, "Power-series solutions of the Lane-Emden equation," Astrophysics and Space Science, vol. 73, pp. 227-239, 1980.
16. N. T. Shawagfeh, "Nonperturbative approximate solution for Lane- Emden equation," J. Math. Phys., vol. 34, pp. 4364-4369, 1993.
17. A.M. Wazwaz, "A new algorithm for solving differential equations of Lane-Emden type," Appl. Math. Comput., vol. 118, pp. 287-310, 2001.
18. A.M. Wazwaz, "The modified decomposition method for analytic treatment of differential equations," Appl. Math. Comput., vol. 173, pp. 165-176, 2006.
19. E. Momoniat, C. Harley, "Approximate implicit solution of a Lane- Emden equation," New Astronomy, vol. 11, pp. 520-526, 2006.
20. J.H. He, "Variational approach to the Lane-Emden equation," Appl. Math. Comput., vol. 143, pp. 539-541, 2003.
21. S. J. Liao, "A new analytic algorithm of Lane-Emden type equations," Appl. Math. Comput., vol. 142, pp. 1-16, 2003.
22. O. P. Singh, R. K. Pandey, V. K. Singh, "An analytic algorithm of LaneEmden type equations arising in astrophysics using modified Homotopy analysis method," Comp. Phys. Commun., vol. 180, pp. 1116-1124, 2009.
23. R. A. Van Gorder, K. Vajravelu, "Analytic and numerical solutions to the Lane-Emden equation," Physics Letters A, vol. 372, pp. 6060-6065, 2008.
24. B. K. Datta, "Analytic solution to the Lane-Emden equation," Nuovo Cimento B, vol. 111, pp. 1385-1388, 1996.
25. A. Yildirim, T. Özis, "Solutions of singular IVPs of Lane-Emden type by homotopy perturbation method," Physics Letters A, vol. 369, pp. 70-76, 2007.
26. A. Rafiq, S. Hussain, M. Ahmed, "General homotopy method for Lane- Emden type differential equations," Int. J. of Appl. Math. and Mech, vol. 5, pp. 75-83, 2009.
27. K. Parand, M. Razzaghi, "Rational Legendre approximation for solving some physical problems on semi-infinite intervals," Phys. Scr., vol. 69, pp. 353-357, 2004.
28. K. Parand, A. Pirkhedri, "Sinc-Collocation method for solving Astrophysics equations," A. New. Astron., doi:10.1016/j.newast.2010.01.001, 2010.
29. S. S. Motsa, P. Sibanda and S. Shateyi, "A new spectral-homotopy analysis method for solving a nonlinear second order BVP," Commun Nonlinear Sci Numer Simulat, vol. 15, pp. 2293-2302, 2010.
30. S. S. Motsa, P. Sibanda, "A new successive linearisation method for the numerical solution of general Falkner-Skan boundary value problems (Periodical style-Submitted for publication)," Computers and Fluids, submitted for publication.
31. S. S. Motsa, Z. Makukula, P. Sibanda, "On the efficient solution of the Von Kármán swirling viscous flow using a simple linearisation technique (Periodical style-Submitted for publication)," Physics Letters A, submitted for publication.
32. C. Canuto, M. Y. Hussaini, A. Quarteroni, and T. A. Zang, Spectral Methods in Fluid Dynamics, Springer-Verlag, Berlin, 1988.
33. W. S. Don, A. Solomonoff, "Accuracy and speed in computing the Chebyshev Collocation Derivative," SIAM J. Sci. Comput, vol. 16, no. 6, pp. 1253-1268, 1995.
34. L. N. Trefethen, Spectral Methods in MATLAB, SIAM, 2000.
35. G. P. Horedt, Polytropes applications in Astrophysics and related fields, Kluwer Academic Publishers, Dordrecht, 2004.