  We propose a computer-assisted approach to studying the effective continuum
behavior of spatially discrete evolution equations. The advantage of the
approach is that the "coarse model" (the continuum, effective equation) need
not be explicitly constructed. The method only uses a time-integration code for
the discrete problem and judicious choices of initial data and integration
times; our bifurcation computations are based on the so-called Recursive
Projection Method (RPM) with arc-length continuation (Shroff and Keller, 1993).
The technique is used to monitor features of the genuinely discrete problem
such as the pinning of coherent structures and its results are compared to
quasi-continuum approaches such as the ones based on Pade approximations.
