Evaluation of Scipy.ode Integrators in Solving the Lane-Emden Equation for Polytropes as a Boundary Value Problem with a Fitting Method
DOI:
https://doi.org/10.12723/mjs.40.5Keywords:
Lane-Emden equation, Two point BVP with fitting method, Scipy ode solversAbstract
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.
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
[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
Additional Files
Published
2017-02-07
Issue
Section
Research Articles
