Numerical methods and error estimates for a singular boundary-value problem

In this paper we analyze a class of equations of the form y? (x) = —g(x) x^p (y(x))^q where p and q are real parameters satisfying p > ^_1, g < ^_1 and g is a positive and continuous function on [0,1]. We search for positive solutions which satisfy the boundary conditions y'(0)=y(l) = 0. Numerical approximations of the solution are obtained by means of a finite difference scheme and the asymptotic expansion of the discretization error is deduced. Some numerical examples are analyzed.