  The Schwinger mechanism of electron-positron pair production in the presence
of strong external electric fields is analyzed numerically for the case of one-
and two-dimensional field configurations where the external field depends both
on time and one spatial coordinate. In order to provide this analysis, a new
efficient numerical approach is developed. The number of particles created is
obtained numerically and also compared with the analytical results for several
exactly solvable one-dimensional backgrounds. For the case of two-dimensional
field configurations the effects of the spatial finiteness are examined, which
confirms their importance and helps us to attest our approach further. The
corresponding calculations are also performed for several more interesting and
nontrivial combinations of temporal and spatial inhomogeneities. Finally, we
discuss the case of a spatially periodic external field when the approach is
particularly productive. The method employed is described in detail.
