  The set of coupled equations for the self-consistent propagator and the field
expectation value is solved numerically with high accuracy in Euclidean space
at zero temperature and in the broken symmetry phase of the phi^4 model.
Explicitly finite equations are derived with the adaptation of the
renormalization method of van Hees and Knoll [H. van Hees, J. Knoll, Phys. Rev.
D65, 025010 (2001)] to the case of non-vanishing field expectation value. The
set of renormalization conditions used in this method leads to the same set of
counterterms obtained recently in A. Patkos, Zs. Szep, Nucl. Phys. A811,
329-352 (2008). This makes possible the direct comparison of the accurate
solution of explicitly finite equations with the solution of renormalized
equations containing counterterms. The numerically efficient way of solving
iteratively these latter equations is obtained by deriving at each order of the
iteration new counterterms which evolve during the iteration process towards
the counterterms determined based on the asymptotic behavior of the converged
propagator. As shown at different values of the coupling, the use of these
evolving counterterms accelerates the convergence of the solution of the
equations.
