  A fast numerical algorithm for the evolution of parton distributions in x
space is described. The method is close in spirit to `brute' force techniques.
The necessary integrals are performed by summing the approximate contributions
from small steps of the integration region. Because it is a numerical
evaluation it shares the advantage with brute force numerical integration that
there are no restrictions placed on the functional form of the distributions to
be evolved. However, an improvement in the approximation technique results in a
significant reduction in the number of integration steps and a savings in time
on the order of three hundred fifty. The method has been implemented for the
structure functions F_2 and g_1 at next-to-leading order.
