  We consider a universe in which inflation commences because of a positive
cosmological constant, the effect of which is progressively screened by the
interaction between virtual gravitons that become trapped in the expansion of
spacetime. Perturbative calculations have shown that screening becomes
non-perturbatively large at late times. In this paper we consider effective
field equations which can be evolved numerically to provide a non-perturbative
description of the process. The induced stress tensor is that of an effective
scalar field which is a non-local functional of the metric. We use the known
perturbative result, constrained by general principles and guided by a physical
description of the screening mechanism, to formulate a class of ansatze for
this functional. A scheme is given for numerically evolving the field equations
which result from a simple ansatz, from the beginning of inflation past the
time when it ends. We find that inflation comes to a sudden end, producing a
system whose equation of state rapidly approaches that of radiation. Explicit
numerical results are presented.
