  The stability of a galaxy model is most easily assessed through N-body
simulation. Particle-mesh codes have been widely used for this purpose, since
they enable the largest numbers of particles to be employed. We show that the
functional expansion technique, originally proposed by Clutton-Brock for other
simulation problems, is in fact superior for stability work. For simulations of
linear evolution it is not much slower than grid methods using the same number
of particles, and reproduces analytical results with much greater accuracy.
This success rests on its ability to represent global modes with a modest
number of basis functions; grid methods may be more effective for other
applications, however. Our conclusions are based on implementations of
functional expansion and grid algorithms for disk galaxies.
