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

    Authors

    K. Boubaker;R. A. Van Gorder

    Comments

    Authors: contact us about adding a copy of your work at [email protected]

    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

    Share

    COinS
     

    Accessibility Statement

    This item was created or digitized prior to April 24, 2027, or is a reproduction of legacy media created before that date. It is preserved in its original, unmodified state specifically for research, reference, or historical recordkeeping. In accordance with the ADA Title II Final Rule, the University Libraries provides accessible versions of archival materials upon request. To request an accommodation for this item, please submit an accessibility request form.