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Year 2019, , 271 - 276, 01.02.2019
https://doi.org/10.31801/cfsuasmas.451619

Abstract

References

  • Lane J. H., 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, Am. J. Sci. Arts (1870), 50, 57-74.
  • Emden R., Gaskugeln: Anwendungen der Mechanischen Wärmetheorie auf Kosmologische und Meteorologische Probleme, Teubner, Leipzig, 1907.
  • Chandrasekhar S., An introduction to the Study of Stellar Structure, The University of Chicago Press, Chicago, 1939.
  • Davis H. T., Introduction to Nonlinear Differential and Integral Equations, Dover Publications, New York, 1962.
  • Horedt G. P., Polytropes Applications in Astrophysics and Related Fields, Kluwer Academic Publishers, Dordrecht, 2004.
  • Seidov S. F., and Kuzakhmedov R. Kh., Solution of the Lane-Emden problem in series, Sov. Astron. (1977), 21, 399-400.
  • Wazwaz A. M., A new algorithm for solving differential equations of Lane-Emden type, Appl. Math. Comput. (2001), 118, 287-310.
  • Liao S., A new analytic algorithm of Lane-Emden type equations, Appl. Math. Comput. (2003), 142, 1-16.
  • Ramos J. I., Series approach to the Lane-Emden equation and comparison with the homotopy perturbation method, Chaos, Solitons & Fractals (2015), 38, 400-408.
  • Mach P., All solutions of the n = 5 Lane-Emden equations, J. Math. Phys. (2012), 53, 062503.
  • Šmarda Z., and Khan Y., An efficient computational approach to solving singular initial value problems for Lane-Emden type equations, J. Comput. Appl. Math. (2015), 290, 65-73.

Classical Way of Looking at the Lane-Emden Equation

Year 2019, , 271 - 276, 01.02.2019
https://doi.org/10.31801/cfsuasmas.451619

Abstract

In this article, the well-known approximate and analytical solutions of the Lane-Emden equation applying Taylor series expansion are derived. To the best of author's knowledge nobody has overcome the singularity of the Lane-Emden equation at the origin as it is carried out here

References

  • Lane J. H., 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, Am. J. Sci. Arts (1870), 50, 57-74.
  • Emden R., Gaskugeln: Anwendungen der Mechanischen Wärmetheorie auf Kosmologische und Meteorologische Probleme, Teubner, Leipzig, 1907.
  • Chandrasekhar S., An introduction to the Study of Stellar Structure, The University of Chicago Press, Chicago, 1939.
  • Davis H. T., Introduction to Nonlinear Differential and Integral Equations, Dover Publications, New York, 1962.
  • Horedt G. P., Polytropes Applications in Astrophysics and Related Fields, Kluwer Academic Publishers, Dordrecht, 2004.
  • Seidov S. F., and Kuzakhmedov R. Kh., Solution of the Lane-Emden problem in series, Sov. Astron. (1977), 21, 399-400.
  • Wazwaz A. M., A new algorithm for solving differential equations of Lane-Emden type, Appl. Math. Comput. (2001), 118, 287-310.
  • Liao S., A new analytic algorithm of Lane-Emden type equations, Appl. Math. Comput. (2003), 142, 1-16.
  • Ramos J. I., Series approach to the Lane-Emden equation and comparison with the homotopy perturbation method, Chaos, Solitons & Fractals (2015), 38, 400-408.
  • Mach P., All solutions of the n = 5 Lane-Emden equations, J. Math. Phys. (2012), 53, 062503.
  • Šmarda Z., and Khan Y., An efficient computational approach to solving singular initial value problems for Lane-Emden type equations, J. Comput. Appl. Math. (2015), 290, 65-73.
There are 11 citations in total.

Details

Primary Language English
Journal Section Review Articles
Authors

Tanfer Tanriverdi 0000-0003-4686-1263

Publication Date February 1, 2019
Submission Date December 9, 2016
Acceptance Date November 27, 2017
Published in Issue Year 2019

Cite

APA Tanriverdi, T. (2019). Classical Way of Looking at the Lane-Emden Equation. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 68(1), 271-276. https://doi.org/10.31801/cfsuasmas.451619
AMA Tanriverdi T. Classical Way of Looking at the Lane-Emden Equation. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. February 2019;68(1):271-276. doi:10.31801/cfsuasmas.451619
Chicago Tanriverdi, Tanfer. “Classical Way of Looking at the Lane-Emden Equation”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68, no. 1 (February 2019): 271-76. https://doi.org/10.31801/cfsuasmas.451619.
EndNote Tanriverdi T (February 1, 2019) Classical Way of Looking at the Lane-Emden Equation. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68 1 271–276.
IEEE T. Tanriverdi, “Classical Way of Looking at the Lane-Emden Equation”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 68, no. 1, pp. 271–276, 2019, doi: 10.31801/cfsuasmas.451619.
ISNAD Tanriverdi, Tanfer. “Classical Way of Looking at the Lane-Emden Equation”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68/1 (February 2019), 271-276. https://doi.org/10.31801/cfsuasmas.451619.
JAMA Tanriverdi T. Classical Way of Looking at the Lane-Emden Equation. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2019;68:271–276.
MLA Tanriverdi, Tanfer. “Classical Way of Looking at the Lane-Emden Equation”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 68, no. 1, 2019, pp. 271-6, doi:10.31801/cfsuasmas.451619.
Vancouver Tanriverdi T. Classical Way of Looking at the Lane-Emden Equation. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2019;68(1):271-6.

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

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