  The studies of Dyson-Schwinger Equations (DSEs) provide us with insights into
nonperturbative phenomenon of quantum field theory. However, DSEs are
essentially an infinite set of coupled Green's functions, it's necessary to
decouple parts of the equations which are thought of major physical importance
to make the solution of these equations possible. Although the results are
model-dependent, no qualitative deviations from exact solutions are expected
with properly chosen truncation scheme. In this article, a globally convergent
numerical method for the solution of the DSEs of QED$_3$ in Euclidean space is
presented. This method can be adapted for more complex problems, however, it
also shows its limitations when adopted in problems such as the searching for
Wigner solutions.
