  We present two methods to include the asymptotic domain of a background
spacetime in null directions for numerical solutions of evolution equations so
that both the radiation extraction problem and the outer boundary problem are
solved. The first method is based on the geometric conformal approach, the
second is a coordinate based approach. We apply these methods to the case of a
massless scalar wave equation on a Kerr spacetime. Our methods are designed to
allow existing codes to reach the radiative zone by including future null
infinity in the computational domain with minor modifications. We demonstrate
the flexibility of the methods by considering both Boyer-Lindquist and ingoing
Kerr coordinates near the black hole. We also confirm numerically predictions
concerning tail decay rates for scalar fields at null infinity in Kerr
spacetime due to Hod for the first time.
