Aproximate analytical solution for the isothermal Lane Emden equation in a spherical geometry

 

Moustafa Aly Soliman¹'² and Yousef Al-Zeghayer¹

 

¹ Chair of Industrial Catalysts, Department of Chemical Engineering, College of Engineering, King Saud University, P.O. Box 800, Riyadh 11421, Saudi Arabia. (moustafa.aly@bue.edu.eg).

² Department of Chemical Engineering, The British University in Egypt, Cairo, Egypt.

 

Received March 2 2015.
Accepted April 16 2015.

 

RESUMEN

Este trabajo obtiene una solución analítica aproximada para la ecuación isoterma de Lane-Emden que modela una esfera isotérmica autogravitante. La solución aproximada se obtiene en términos de parámetros de distancias pequeños y grandes por el método de perturbaciones. La solución aproximada se compara con la solución numérica. La solución aproximada obtenida es válida para todos los valores del parámetro de distancia.

 

ABSTRACT

This paper obtains an approximate analytical solution for the isothermal Lane-Emden equation that models a self-gravitating isothermal sphere. The approximate solution is obtained by perturbation methods in terms of small and large distance parameters. The approximate solution is compared with the numerical solution. The approximate solution obtained is valid for all values of the distance parameter.

Key Words: stars: formation — stars: general.

 

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REFERENCES

Adler J. 2011, IMA JMA, 76, 817        [ Links ]

Aris R. 1975, The Mathematical Theory of Diffusion and Reaction in permeable Catalyst, Oxford        [ Links ]

Boyd J. P. 2011, ApMaC, 217, 5553        [ Links ]

Britz D., Strutwolf J., & Osterby J. 2011, ApMaC, 218, 1280        [ Links ]

Chandrasekhar S. 1967, An Introduction to the Study of Stellar Structure, New York: Dover Publications        [ Links ]

Chandrasekhar S. & Wares, G. W. 1949, ApJ, 109 Enig,         [ Links ] J. W. 1967, CoFl, 10, 197        [ Links ]

Frank-Kamenetski D. A. 1955, Diffusion and Heat Exchange in Chemical Kinetics, Princeton University Press, Princeton, NJ        [ Links ]

Harley, C. & Momoniat E. 2008, JNMP, 15, 69        [ Links ]

Hlavacek V. & Marek M. 1968, ChEnS, 23, 865        [ Links ]

Horedt G. P. 1986, Ap & SS, 126, 357        [ Links ]

Hunter, C. 2001, MNRAS, 328, 839        [ Links ]

Iacono R. & De Felice M. 2014, CeMDA, 118, 291        [ Links ]

Liu F. K. 1996, MNRAS, 281, 1197        [ Links ]

Mirza B. M. 2009, MNRAS, 395, 2288        [ Links ]

Avygdor, M. & Huw O. Pritchard 1989, CaJch, 67, 442        [ Links ]

Nazari-Golshan A., Nourazar S. S., Ghafoori-Fard H., Yildirim A., & Campo A., 2013, ApMaL, 26, 1018        [ Links ]

Petzold L. 1982, A Description of DASSL A differential/ algebraic system solver, SAND 82-8637 (September)        [ Links ]

Raga, A. C., Rodriguez-Ramirez, J. C., Villasante, M., Rodriguez-Gonzalez, A., & Lora, V. 2013, RMxAA, 49, 63        [ Links ]

Soliman, M. A. 2013, IJET, 13, 24        [ Links ]

Soliman, M. A., 2013, in Advances in applied mathematics, ed. Ali R. Ansari, (New York, Springer) 223        [ Links ]

Steggerda J. J. 1965, J. Chem. Phys., 43, 4446        [ Links ]