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New Analytic Solution to the Lane-Emden Equation of Index 2

机译：索引2的Lane-Emden方程的新解析解

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摘要

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 Horedt (1986) 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.
机译：我们提出了两种新的解析方法，用于解决初值问题，这些问题在天体物理学和数学物理学中为多变和恒星结构建模。该方法的适用性，有效性和可靠性通过用二阶非线性微分方程描述的Lane-Emden方程进行评估。在这项工作中获得的结果也与Horedt（1986）的数值结果进行了比较，后者被广泛用作测试新方法的基准。在当前结果和数值结果之间观察到良好的一致性。还对提出的新方法与现有分析方法进行了比较，发现新方法比某些现有分析方法更有效并且具有一些优势。

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  • 来源
    《Mathematical Problems in Engineering》 |2012年第4期|p.614796.1-614796.19|共19页
  • 作者

    S. S. Motsa; S. Shateyi;

  • 作者单位

    School of Mathematical Sciences, University of KwaZulu-Natal, Private Bag X01, Pietermaritzburg, Scottsville 3209, South Africa;

    Department of Mathematics, University of Venda, Private Bag X5050, Thohoyandou 0950, South Africa;

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