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Year 2019, Volume: 68 Issue: 1, 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, Volume: 68 Issue: 1, 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 Volume: 68 Issue: 1

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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