An approximate solution for the polytrope N = 3

Details An approximate solution for the polytrope N = 3 An approximate solution for the polytrope N = 3

Apr 1987

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1987ap%26ss.132..393b&link_type=abstract

Astrophysics and Space Science (ISSN 0004-640X), vol. 132, no. 2, April 1987, p. 393-396.

Computer Science

Numerical Analysis

1

Polytropic Processes, Stellar Interiors, Stellar Models, Approximation, Gravitational Effects, Numerical Analysis

Scientific paper

In general, the Lane-Emden equation for an arbitrary polytropic index n does not admit of an analytic solution. Simple approximation to the numerical results can, however, be found; and, in particular, θ(x) = sech(x/√3) affords a hitherto unreported good approximation to the n = 3 model. This term is accurate to within 10% of the tabulated values over 78% of the polytropic interior.

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