  Dirac equation for an electron bound by a nucleus in the presence of external
axially symmetric field can be solved numerically by using the
dual-kinetic-balance conditions imposed on the finite basis set (A-DKB method
[Rozenbaum et al, Phys. Rev. A 89, 012514 (2014)]). We present the application
of this method to describe helium-like ions exposed to homogeneous external
magnetic field. The second-order Zeeman shift and the nuclear magnetic
shielding constant are evaluated for the ground state, including the leading
contribution of the interelectronic interaction. The A-DKB values are compared
with the direct calculations by perturbation theory. The results for the
nuclear magnetic shielding can serve for accurate determination of the nuclear
magnetic moments. The quadratic contribution to the Zeeman effect can be
relevant for high-precision measurements of the transition energies in
helium-like ions.
