Numerical solution of integro-differential equations arising from singular boundary value problems

We consider the numerical solution of a singular boundary value problem on the half line for a second order nonlinear ordinary differential equation. Due to the fact that the nonlinear differential equation has a singularity at the origin and the boundary value problem is posed on an unbounded domain, the proposed approaches are complex and require a considerable computational effort. In the present paper, we describe an alternative approach, based on the reduction of the original problem to an integro-differential equation. Though the problem is posed on the half-line, we just need to approximate the solution on a finite interval. By analyzing the behavior of the numerical approximation on this interval, we identify the solution that satisfies the prescribed boundary condition. Although the numerical algorithm is much simpler than the ones proposed before, it provides accurate approximations. We illustrate the proposed methods with some numerical examples.