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Publication Details
AFRICAN RESEARCH NEXUS
SHINING A SPOTLIGHT ON AFRICAN RESEARCH
earth and planetary sciences
Approximate implicit solution of a Lane-Emden equation
New Astronomy, Volume 11, No. 7, Year 2006
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Description
In this paper, we obtain an approximate implicit solution admitted by the Lane-Emden equation y″ + (2/x)y′ + ey = 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. © 2006 Elsevier B.V. All rights reserved.
Authors & Co-Authors
Momoniat, Ebrahim
South Africa, Johannesburg
University of the Witwatersrand
Harley, Charis
South Africa, Johannesburg
University of the Witwatersrand
Statistics
Citations: 83
Authors: 2
Affiliations: 1
Identifiers
Doi:
10.1016/j.newast.2006.02.004
ISSN:
13841076