  In previous work, the numerical solution of the linearized gravitational
field equations near space-like and null-infinity was discussed in the form of
the spin-2 zero-rest-mass equation for the perturbations of the conformal Weyl
curvature. The motivation was to study the behavior of the field and properties
of the numerical evolution of the system near infinity using Friedrich's
conformal representation of space-like infinity as a cylinder. It has been
pointed out by H.O. Kreiss and others that the numerical evolution of a system
using second order wave equations has several advantages compared to a system
of first order equations. Therefore, in the present paper we derive a system of
second order wave equations and prove that the solution spaces of the two
systems are the same if appropriate initial and boundary data are given. We
study the properties of this system of coupled wave equations in the same
geometric setting and discuss the differences between the two approaches.
