  Some results of the ongoing development of our Source Galerkin (SG)
nonperturbative approach to numerically solving Quantum Field theories are
presented. This technique has the potential to be much faster than Monte Carlo
methods. SG uses known symmetries and theoretical properties of a theory. In
order to test this approach, we applied it to phi^4 theory in zero dimensions.
This model has been extensively studied and has a known set of exact solutions.
This allows us to broaden the understanding of various properties of the SG
method and to develop techniques necessary for the successful application of
this method to more sophisticated theories.
