A scheme to numerically evolve data for the conformal Einstein equation

This is the second paper in a series describing a numerical implementation of the conformal Einstein equation. This paper deals with the technical det ails of the numerical code used to perform numerical time evolutions from a 'minimal' set of data. We outline the numerical construction of a complete set of data for our equ ations from a minimal set of data. The second- and the fourth-order discret izations, which are used for the construction of the complete data set and for the numerical integration of the time evolution equations, are describe d and their efficiencies are compared. By using the fourth-order scheme we reduce our computer resource requirements-with respect to memory as well as computation time-by at least two orders of magnitude as compared to the se cond-order scheme.