We now construct a simplified model, that retains the main features of (14). We approximate all functions u(x), v(x) and w(x) by piecewise constant functions, taking, at each time instant only two values at two different and fixed parts of the membrane. Denoting the two parts of the membrane by indices + and -, system (14) is then rewritten in the form
where the signs in the last two equations are either all + or -.
In writing this system, we have taken into account the main properties of
and 
listed in the previous section. The constant 
of the dimensionality of conductivity in (15) should be
positive; it is the effective conductivity of the cell in this
two-compartment approximation. 
is the current produced by the
external source and crossing the cell.
