We conduct a series of magnetohydrodynamical (MHD) simulations of magnetized
interstellar medium (ISM) disturbed by exploding stars. We assume that
exploding stars deposit small-scale, randomly oriented, dipolar magnetic
fields into the differentially rotating ISM, together with a portion of cosmic
rays, accelerated in supernova shocks. Our simulations are performed with the
aid of a new MHD code PIERNIK, in the shearing box approximation, and in a
global galactic disk. We demonstrate that the small scale, dipolar magnetic
field contributions evolve, in presence of buoyancy effects, towards a large
scale magnetic field component in galactic disks. We find that the initial
magnetization of galactic disks by exploding magnetized stars forms a favourable
initial condition for the cosmic-ray driven dynamo. The amplification timescale
of the large-scale magnetic field, resulting from the ovarall process, is
comparable to the galactic rotation period.