Skip to main content
Log in

Taylor series solution for Lane–Emden equation

  • Original Paper
  • Published:
Journal of Mathematical Chemistry Aims and scope Submit manuscript

Abstract

Taylor series is accessible to all students and it is a useful mathematical tool to nonlinear equations. This paper shows it is extremely simple to solve approximately the well-known Lane–Emden equation.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. P. Roul, A new mixed MADM-Collocation approach for solving a class of Lane–Emden singular boundary value problems. J. Math. Chem. 57, 945–969 (2019)

    Article  CAS  Google Scholar 

  2. H. Madduri, P. Roul, A fast-converging iterative scheme for solving a system of Lane–Emden equations arising in catalytic diffusion reactions. J. Math. Chem. 57, 570–582 (2019)

    Article  CAS  Google Scholar 

  3. T.C. Hao, F.Z. Cong, Y.F. Shang, An efficient method for solving coupled Lane–Emden boundary value problems in catalytic diffusion reactions and error estimate. J. Math. Chem. 56, 2691–2706 (2018)

    Article  CAS  Google Scholar 

  4. A.K. Verma, S. Kayenat, On the convergence of Mickens’ type nonstandard finite difference schemes on Lane–Emden type equations. J. Math. Chem. 56, 1667–1706 (2018)

    Article  CAS  Google Scholar 

  5. A.M. Wazwaz, Solving the non-isothermal reaction–diffusion model equations in a spherical catalyst by the variational iteration method. Chem. Phys. Lett. 679, 132–136 (2017)

    Article  CAS  Google Scholar 

  6. J.H. He, Variational approach to the Lane–Emden equation. Appl. Math. Comput. 143(2–3), 539–541 (2003)

    Google Scholar 

  7. Y. Wu, J.H. He, Homotopy perturbation method for nonlinear oscillators with coordinate dependent mass. Results Phys. 10, 270–271 (2018)

    Article  Google Scholar 

  8. Z.J. Liu, M.Y. Adamu, E. Suleiman et al., Hybridization of homotopy perturbation method and Laplace transformation for the partial differential equations. Therm. Sci. 21, 1843–1846 (2017)

    Article  Google Scholar 

  9. M.Y. Adamu, P. Ogenyi, New approach to parameterized homotopy perturbation method. Therm. Sci. 22(4), 1865–1870 (2018)

    Article  Google Scholar 

  10. N. Anjum, J.H. He, Laplace transform: making the variational iteration method easier. Appl. Math. Lett. 92, 134–138 (2019)

    Article  Google Scholar 

  11. J.H. He, Some asymptotic methods for strongly nonlinear equations. Int. J. Mod. Phys. B 20, 1141–1199 (2006)

    Article  Google Scholar 

  12. L.J. Xie, C.L. Zhou, S. Xu, Solving the systems of equations of Lane-Emden type by differential transform method coupled with adomian polynomials. Mathematics 7(4), 377 (2019)

    Article  Google Scholar 

  13. J.H. He, A tutorial review on fractal spacetime and fractional calculus. Int. J. Theor. Phys. 53(11), 3698–3718 (2014)

    Article  Google Scholar 

  14. J.H. He, Fractal calculus and its geometrical explanation. Results Phys. 10, 272–276 (2018)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Ji-Huan He.

Additional information

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

He, JH., Ji, FY. Taylor series solution for Lane–Emden equation. J Math Chem 57, 1932–1934 (2019). https://doi.org/10.1007/s10910-019-01048-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10910-019-01048-7

Keywords

Navigation