  A simple and reliable finite difference approach is presented for solution of
the Dirac equation eigenproblem for states confined in rotationally symmetric
systems. The method sets the boundary condition for the spinor wave function
components at the external edge of the system and then sweeps the radial mesh
in search for the energies for which the boundary conditions are met inside the
flake. The sweep that is performed from the edge of the system towards the
origin allows for application of a two-point finite difference quotient of the
first derivative, which prevents the fermion doubling problem and the
appearance of the spurious solutions with rapid oscillations of the wave
functions in space.
