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

Authors:
P. M. Lima;A. M. Oliveira
Affiliations:
Instituto Superior Técnico, Departamento de Matemática, Av. Rovisco Pais, 1049-001 Lisboa, Portugal;Faculdade de Ciências e Tecnologia, Departamento de Matemática, Quinta da Torre, 2829-516 Caparica, Portugal
Venue:
Applied Numerical Mathematics
Year:
2003

Citing 3
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Abstract

In this paper we shall deal with an equation of the form y" (x) = -g(x)xp (y(x))q, where p and q are real parameters satisfying p -2, q 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.