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New analytic solution to the Lane-Emden equation of index 2. (English) Zbl 1264.65130
Summary: We present two new analytic methods that are used for solving initial value problems that model polytropic and stellar structures in astrophysics and mathematical physics. The applicability, effectiveness, and reliability of the methods are assessed on the Lane-Emden equation which is described by a second-order nonlinear differential equation. The results obtained in this work are also compared with numerical results of G. P. Horedt [“Seven-digit tables of Lane-Emden functions,” Astrophy. Space Sci. 126, No. 2, 357–408 (1986; doi:10.1007/BF00639386)] which are widely used as a benchmark for testing new methods of solution. Good agreement is observed between the present results and the numerical results. Comparison is also made between the proposed new methods and existing analytical methods and it is found that the new methods are more efficient and have several advantages over some of the existing analytical methods.

MSC:
65L99 Numerical methods for ordinary differential equations
34A45 Theoretical approximation of solutions to ordinary differential equations
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