Evaluation of Scipy.ode Integrators in Solving the Lane-Emden Equation for Polytropes as a Boundary Value Problem with a Fitting Method

  • M N Anandaram Bangalore University
Keywords: Lane-Emden equation, Two point BVP with fitting method, Scipy ode solvers

Abstract

The use of Scipy integrators like dopri5 and others in accurately solving the  Lane-Emden equation of a polytrope as a two-point BVP with fitting is investigated by comparing the Emden radius with the extended precision reference value obtained by Boyd's Chebyshev spectral method. It is found that both dopri5 and dop853 integrators provide acceptable accuracy upto 14 decimal digits.

Author Biography

M N Anandaram, Bangalore University

Professor of Physics ,  Bangalore University

References

[1] M.N. Anandaram, "On Emden's Polytropes: Gas Globes in Hydrostatic Equilibrium", Mapana J Sci, Vol.12, No. 1, pp. 85-114, 2014.
[2] http://bender.astro.sunysb.edu/classes/stars/notes/models.pdf
[3] http://bender.astro.sunysb.edu/classes/stars/notes/le-fit.py
[4] J.P. Boyd, "Chebyshev Spectral Methods and the Lane-Emden Problem", Numer. Math. Theor. Meth. Appl., Vol. 4, No. 2, pp. 142-157, 2011.
[5] https://github.com/nikola-m/another-chebpy/blob/master/boyd_polytropes.py
Published
2017-02-07
Section
Research Articles