  We use the overlapping grids method to construct a fourth order accurate
discretization of a first order reduction of the Klein-Gordon scalar field
equation on a boosted spinning black hole blackground in axisymmetry. This
method allows us to use a spherical outer boundary and excise the singularity
from the domain with a spheroidal inner boundary which is moving with respect
to the main grid. We discuss the use of higher order accurate energy conserving
schemes to handle the axis of symmetry and compare it with a simpler technique
based on regularity conditions. We also compare the single grid long term
stability property of this formulation of the wave equation with that of a
different first order reduction.
