  Pion-nucleus scattering cross sections are calculated by solving a
Schr\"{o}dinger equation reduced from the Klein-Gordon equation. Local
potentials are assumed, and phenomenological potential parameters are searched
energy-dependently for $\pi^{-} + ^{12}$C system so as to reproduce not only
elastic differential cross sections but also total elastic, reaction and total
cross sections at 13 pion incident energies from 120 to 766 MeV. The real and
imaginary parts of the local potentials thus obtained are shown to satisfy the
dispersion relation. The imaginary part of the potentials as a function of the
pion energy is found to peak near the $\Delta$(1232)-resonance energy. The
strong absorption radius of the pion projectile with incident energies near the
$\Delta$-resonance region is found to be about $1.6 A^{1/3}$ fm, which is
consistent with previous studies of the region where the decay of the
$\Delta$'s takes place in nuclei. The phenomenological local potentials are
then compared with the local potentials exactly phase-shift equivalent to
Kisslinger potentials for pion energies near the $\Delta$-resonance.
