  In general-relativistic perturbation theory, a point mass accelerates away
from geodesic motion due to its gravitational self-force. Because the
self-force is small, one can often approximate the motion as geodesic. However,
it is well known that self-force effects accumulate over time, making the
geodesic approximation fail on long timescales. It is less well known that this
failure at large times translates to a failure at large distances as well. At
second perturbative order, two large-distance pathologies arise: spurious
secular growth and infrared-divergent retarded integrals. Both stand in the way
of practical computations of second-order self-force effects.
  Utilizing a simple flat-space scalar toy model, I develop methods to overcome
these obstacles. The secular growth is tamed with a multiscale expansion that
captures the system's slow evolution. The divergent integrals are eliminated by
matching to the correct retarded solution at large distances. I also show how
to extract conservative self-force effects by taking local-in-time "snapshots"
of the global solution. These methods are readily adaptable to the physically
relevant case of a point mass orbiting a black hole.
