  A new approach for solving the time-dependent two-center Dirac equation is
presented. The method is based on using the finite basis set of cubic Hermite
splines on a two-dimensional lattice. The Dirac equation is treated in rotating
reference frame. The collision of U92+ (as a projectile) and U91+ (as a target)
is considered at energy E_lab=6 MeV/u. The charge transfer probabilities are
calculated for different values of the impact parameter. The obtained results
are compared with the previous calculations [I. I. Tupitsyn et al., Phys. Rev.
A 82, 042701 (2010)], where a method based on atomic-like Dirac-Sturm orbitals
was employed. This work can provide a new tool for investigation of quantum
electrodynamics effects in heavy-ion collisions near the supercritical regime.
