  A general method for solving numerically the time-dependent Schr\"odinger
equation, that is based on the Suzuki-Trotter scheme with the split-step
Fourier approach, is introduced. The method relies on a Hamiltonian
decomposition, where except of the components depending exclusively on the
momentum or on the position operators, there are also terms depending on both
momentum and position operators in particular configurations. We demonstrate
that, for as long as the latter does not depend on noncommuting coordinates of
the momentum and position operators, nondipole effects in laser-matter
interactions can be studied without applying extra unitary operations.
Specifically, we analyze the effect of nondipole corrections in ionization of a
two-dimensional hydrogen atom for low- and high-frequency pulses. In the former
case, the electron wave packet dynamics is dominated by rescattering processes
within the laser pulse, leading to the high-order harmonic generation. We
illustrate that harmonics of even orders are generated in the direction of the
laser field polarization. On the contrary, for high-frequency pulses, such
rescattering processes can be neglected. We demonstrate that a significant
portion of the low-energy photoelectrons is detected opposite to the laser
pulse propagation direction as a consequence of their post-pulse wave packet
spreading and interaction with the parent ion.
