Computing Eigenfunctions of Singular Points in Nonlinear Parametrized Two-Point BVPs

The iterative computation of singular points in parametrized nonlinear BVPs by so-called extended systems requires good starting values for the singular point itself and the corresponding eigenfunction. Using path-following techniques such starting values for the singular points should be generated automatically. However, pathfollowing does not provide approximations for the eigenfunctions. We propose a new modification of this standard technique delivering such starting values. It is based on an extended system by which singular as well as nonsingular points can be determined.