  Based upon elements of the modern Pseudoanalytic Function Theory, we analyse
a new method for numerically approaching the solution of the Dirichlet boundary
value problem, corresponding to the two-dimensional Electrical Impedance
Equation. The analysis is performed by interpolating piecewise
separable-variables conductivity functions, that are eventually used in the
numerical calculations in order to obtain finite sets of orthonormal functions,
whose linear combinations succeed to approach the imposed boundary conditions.
To warrant the effectiveness of the numerical method, we study six different
examples of conductivity. The boundary condition for every case is selected
considering one exact solution of the Electrical Impedance Equation. The work
intends to discuss the contributions of these results into the field of the
Electrical Impedance Tomography.
