  We present the results of standard one-dimensional test problems in
relativistic hydrodynamics using Glimm's (random choice) method, and compare
them to results obtained using finite differencing methods. For problems
containing profiles with sharp edges, such as shocks, we find Glimm's method
yields global errors ~1-3 orders of magnitude smaller than the traditional
techniques. The strongest differences are seen for problems in which a shear
field is superposed. For smooth flows, Glimm's method is inferior to standard
methods. The location of specific features can be off by up to two grid points
with respect to an exact solution in Glimm's method, and furthermore curved
states are not modeled optimally since the method idealizes solutions as being
composed of piecewise constant states. Thus although Glimm's method is superior
at correctly resolving sharp features, especially in the presence of shear, for
realistic applications in which one typically finds smooth flows plus strong
gradients or discontinuities, standard FD methods yield smaller global errors.
Glimm's method may prove useful in certain applications such as GRB afterglow
shock propagation into a uniform medium.
