  Employing a limiting case of a conjecture for constructing piecewise
separable-variables functions, the elements of the Pseudoanalytic Function
Theory are used for numerically approaching solutions of the forward Dirichlet
boundary value problem, corresponding to the Electrical Impedance Equation in
the plane, when the electrical conductivity is an arbitrary non-vanishing
function, fully defined within a bounded domain. The new method is studied
considering a variety of examples when the bounded domain coincides with the
unit circle, and it is also included a description of its behaviour in
non-smooth domains, selecting special cases that do not require additional
regularization techniques, for warranting the convergence of the approach at
the non-smooth regions, when certain requirements are fulfilled.
