  A new method for solving the time-dependent two-center Dirac equation is
developed. The approach is based on the using of the finite basis of cubic
Hermite splines on a three-dimensional lattice in the coordinate space. The
relativistic calculations of the excitation and charge-transfer probabilities
in the U91+(1s)-U92+ collisions in two and three dimensional approaches are
performed. The obtained results are compared with our previous calculations
employing the Dirac-Sturm basis sets [I.I. Tupitsyn et al., Phys. Rev. A 82,
042701 (2010)]. The role of the negative-energy Dirac spectrum is investigated
within the monopole approximation.
