Numericalmethods for Volterra integral equations with discontinuous kernel need to be tuned to their peculiar form. Here we propose a version of the trapezoidal direct quadrature method adapted to such a type of equations. In order to delineate its stability properties, we first investigate about the behavior of the solution of a suitable (basic) test equation and then we find out under which hypotheses the trapezoidal direct quadrature method provides numerical solutions which inherit the properties of the continuous problem.
Volterra integral equations
Trapezoidal method
Direct quadrature methods
Discontinuous kernel
Constant delay
A single master equation is given describing spin s=2 test fields that are gaugeand
tetrad-invariant perturbations of the spinning C metric space-time representing
a source with mass M, uniformly rotating with angular momentum per unit mass a,
and uniformly accelerated with acceleration A. This equation can be separated into
its radial and angular parts. The behavior of the radial functions near the black hole
outer horizon is studied to examine the influence of A on the phenomenon of
super-radiance, while the angular equation leads to modified spin-weighted spheroidal
harmonic solutions generalizing those of the Kerr space-time. Finally the
coupling between the spin of the perturbing field and the acceleration parameter A
is discussed.
