  We outline two alternative schemes to perform numerical calculations in
quantum field theory. In principle, both of these approaches are better suited
to study phase structure than conventional Monte Carlo. The first method,
Source Galerkin, is based on a numerical analysis of the Schwinger-Dyson
equations using modern computer techniques. The nature of this approach makes
dealing with fermions relatively straightforward, particularly since we can
work on the continuum. Its ultimate success in non-trivial dimensions will
depend on the power of a propagator expansion scheme which also greatly
simplifies numerical calculation of traditional perturbation graphs. The second
method extends Monte Carlo approaches by introducing a procedure to deal with
rapidly oscillating integrals.
