Numerical solution of a singular boundary value problem for a generalized Emden-Fowler equation

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Abstract

In this paper we shall deal with an equation of the form y″(x)=-g(x)xpy(x)q, where p and q are real parameters satisfying p < -2, q < -1 and g is a positive and continuous function on [0,1]. We shall search for positive solutions which satisfy the boundary conditions: y(0)=y(1)=0. The initial nonlinear problem is transformed into a sequence of linear ones, each one of them is approximated by a finite difference scheme. Asymptotic expansions of the error are obtained and numerical examples are then analysed.

Original languageEnglish
Pages (from-to)389-409
Number of pages21
JournalApplied Numerical Mathematics
Volume45
Issue number4
DOIs
Publication statusPublished - Jun 2003

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