Application of the BPES to Lane-Emden equations governing polytropic and isothermal gas spheres

    Authors

    K. Boubaker;R. A. Van Gorder

    Comments

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    Abbreviated Journal Title

    New Astron.

    Keywords

    Analytical methods; Stellar interiors; Lane-Emden equations; POLYNOMIALS EXPANSION SCHEME; VARIATIONAL ITERATION METHOD; BOUBAKER; POLYNOMIALS; 2ND KIND; KEYHOLE MODEL; 1ST INTEGRALS; Astronomy & Astrophysics

    Abstract

    We apply the Boubaker Polynomials Expansion Scheme (BPES) in order to obtain analytical-numerical solutions to two separate Lane-Emden problems: the Lane-Emden initial value problem of the first kind (describing the gravitational potential of a self-gravitating spherically symmetric polytropic gas), the Lane-Emden initial value problem of the second kind (describing isothermal gas spheres embedded in a pressurized medium at the maximum possible mass allowing for hydrostatic equilibrium). Both types of problems are simultaneously singular and nonlinear, and hence can be challenging to solve either numerically or analytically. We find that the BPES allows us to compute numerical solutions to both types of problems, and an error analysis demonstrates the accuracy of the method. In all cases, we demonstrate that relative error can be controlled to less than 1%. Furthermore, we compare our results to those of Hunter (2001). [Hunter, C., 2001. Series solutions for polytropes and the isothermal sphere. Monthly Notices of the Royal Astronomical Society, 328 839-847] and Mirza (2009). Approximate analytical solutions of the Lane-Emden equation for a self-gravitating isothermal gas sphere. Monthly Notices of the Royal Astronomical Society, 395 2288-2291. in order to demonstrate the accuracy of our method. (C) 2012 Elsevier B.V. All rights reserved.

    Journal Title

    New Astronomy

    Volume

    17

    Issue/Number

    6

    Publication Date

    1-1-2012

    Document Type

    Article

    Language

    English

    First Page

    565

    Last Page

    569

    WOS Identifier

    WOS:000303099500002

    ISSN

    1384-1076

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