  We present details of a new numerical code designed to study the formation
and evaporation of 2-dimensional black holes within the CGHS model. We explain
several elements of the scheme that are crucial to resolve the late-time
behavior of the spacetime, including regularization of the field variables,
compactification of the coordinates, the algebraic form of the discretized
equations of motion, and the use of a modified Richardson extrapolation scheme
to achieve high-order convergence. Physical interpretation of our results will
be discussed in detail elsewhere.
