Approximate implicit solution of a Lane-Emden equation

被引：67

作者：

Momoniat, E ^{[1
]}

Harley, C ^{[1
]}

机构：

[1] Univ Witwatersrand, Ctr Differential Equat, Continuum Mech & Applicat Sch Computat & Appl Mat, ZA-2050 Johannesburg, South Africa

来源：

NEW ASTRONOMY | 2006年 / 11卷 / 07期

基金：

新加坡国家研究基金会;

关键词：

isothermal gas sphere; Lane-Emden equation; Lie group method; approximate implicit solution;

D O I：

10.1016/j.newast.2006.02.004

中图分类号：

P1 [天文学];

学科分类号：

0704 ;

摘要：

In this paper, we obtain an approximate implicit solution admitted by the Lane-Emden equation y(n) + (2/x)y' + e(y) = 0 describing the dimensionless density distribution in an isothermal gas sphere. The new approximate implicit solution has a larger radius of convergence than the power series solution. This is achieved by reducing the Lane-Emden equation to first-order using Lie group analysis and determining a power series solution of the reduced equation. The power series solution of the reduced equation transforms into an approximate implicit solution of the original equation. The approximate implicit solution diverges from the power series solution in the radius of convergence. (c) 2006 Elsevier B.V. All rights reserved.

引用

页码：520 / 526

页数：7

共 22 条

[1] HIDDEN SYMMETRIES ASSOCIATED WITH THE PROJECTIVE GROUP OF NONLINEAR 1ST-ORDER ORDINARY DIFFERENTIAL-EQUATIONS [J].