  We present a new approach to calculate the particle distribution function
about relativistic shocks including synchrotron losses using the method of
lines with an explicit finite difference scheme. A steady, continuous, one
dimensional plasma flow is considered to model thick (modified) shocks, leading
to a calculation in three dimensions plus time, the former three being
momentum, pitch angle and position. The method accurately reproduces the
expected power law behaviour in momentum at the shock for upstream flow speeds
ranging from 0.1c to 0.995c (1 < \Gamma < 10). It also reproduces approximate
analytical results for the synchrotron cutoff shape for a non-relativistic
shock, demonstrating that the loss process is accurately represented. The
algorithm has been implemented as a hybrid OpenMP--MPI parallel algorithm to
make efficient use of SMP cluster architectures and scales well up to many
hundreds of CPUs.
