  A spectral parameter power series (SPPS) representation for the regular
solution of the radial Dirac system with complex coefficients is obtained, as
well as a SPPS representation for the (entire) characteristic function of the
corresponding spectral problem on a finite interval. Based on the SPPS
representation, a numerical method for solving spectral problems is developed.
It is shown that the method is also applicable to solving spectral problems for
perturbed Bessel equations. We exhibit that the proposed numerical method
delivers excellent results. Additionally, an application of the method to find
the energy values of hydrogen-like atoms with a finite radius is presented.
