Instability of invariant boundary conditions of a generalized Lane-Emden equation of the second-kind

C. Harley, E. Momoniat

Research output: Contribution to journalArticlepeer-review

9 Citations (Scopus)

Abstract

A generator of Lie point symmetries admitted by a Lane-Emden equation of the second-kind for arbitrary shape factor k is used to determine invariant boundary conditions admitted by the equation. The generator of Lie point symmetries is then used to reduce the order of the Lane-Emden equation. A phase plane analysis of the reduced equation indicates that the stability of the invariant boundary condition y = 0 on the line x = 0 changes with changing shape factor k. We show that for values of the shape factor k > 1 the boundary condition y = 0 is stable on the line x = 0 while it is unstable for k ≤ 1.

Original languageEnglish
Pages (from-to)621-633
Number of pages13
JournalApplied Mathematics and Computation
Volume198
Issue number2
DOIs
Publication statusPublished - 1 May 2008
Externally publishedYes

Keywords

  • Invariant boundary condition
  • Lane-Emden equation
  • Lie group method
  • Phase plane analysis
  • Stability

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

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