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

Numerical solution of the relativistic single-site scattering problem for the Coulomb and the Mathieu potential