  For a reliable fully-relativistic Korringa-Kohn-Rostoker Green function
method, an accurate solution of the underlying single-site scattering problem
is necessary. We present an extensive discussion on numerical solutions of the
related differential equations by means of standard methods for a direct
solution and by means of integral equations. Our implementation is tested and
exemplarily demonstrated for a spherically symmetric treatment of a Coulomb
potential and for a Mathieu potential to cover the full-potential
implementation. For the Coulomb potential we include an analytic discussion of
the asymptotic behaviour of irregular scattering solutions close to the origin
($r\ll1$).
