  We study the evolution of spherically symmetric radiating fluid distributions
using the effective variables method, implemented {\it ab initio} in
Schwarzschild coordinates. To illustrate the procedure and to establish some
comparison with the original method, we integrate numerically the set of
equations at the surface for two different models. The first model is derived
from the Schwarzschild interior solution. The second model is inspired in the
Tolman VI solution.
