Analytic and numerical solutions to the Lane-Emden equation

    Authors

    R. A. Van Gorder;K. Vajravelu

    Comments

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    Abbreviated Journal Title

    Phys. Lett. A

    Keywords

    Lane-Emden equation; Gravitational potential; Nonlinear ordinary; differential equation; Analytical solution; Numerical Solution; HOMOTOPY ANALYSIS METHOD; Physics, Multidisciplinary

    Abstract

    In this Letter, we present analytical solutions to the Lane-Emden equation y ''(x) + 2/xy'(x) + f(y) = 0 describing the thermal behavior of a spherical cloud of gas acting under the mutual attraction of its molecules. Solutions are obtained by using the traditional power series approach and by using the Homotopy Analysis Method (HAM). We show that the series solutions obtained by the Homotopy Analysis Method converge in a larger interval than in the case of the corresponding traditional series solutions. Furthermore, we obtained numerical solutions (using Runge-Kutta-Fehlberg 4-5 technique) which are used to validate the analytical solutions. (c) 2008 Elsevier B.V. All rights reserved.

    Journal Title

    Physics Letters A

    Volume

    372

    Issue/Number

    39

    Publication Date

    1-1-2008

    Document Type

    Article

    Language

    English

    First Page

    6060

    Last Page

    6065

    WOS Identifier

    WOS:000260063700004

    ISSN

    0375-9601

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