TY - JOUR
T1 - Numerical solution of a singular boundary value problem for a generalized Emden-Fowler equation
AU - Lima, Pedro Miguel
AU - Oliveira, António Manuel Morais Fernandes de
PY - 2003/6
Y1 - 2003/6
N2 - 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.
AB - 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.
KW - expansions
UR - http://www.scopus.com/inward/record.url?scp=0038219596&partnerID=8YFLogxK
U2 - 10.1016/S0168-9274(02)00252-0
DO - 10.1016/S0168-9274(02)00252-0
M3 - Article
SN - 0168-9274
VL - 45
SP - 389
EP - 409
JO - Applied Numerical Mathematics
JF - Applied Numerical Mathematics
IS - 4
ER -