  We have developed a new, very efficient numerical scheme to solve the CR
diffusion convection equation that can be applied to the study of the nonlinear
time evolution of CR modified shocks for arbitrary spatial diffusion
properties. The efficiency of the scheme derives from its use of coarse-grained
finite momentum volumes. This approach has enabled us, using $\sim 10 - 20$
momentum bins spanning nine orders of magnitude in momentum, to carry out
simulations that agree well with results from simulations of modified shocks
carried out with our conventional finite difference scheme requiring more than
an order of magnitude more momentum points. The coarse-grained, CGMV scheme
reduces execution times by a factor approximately half the ratio of momentum
bins used in the two methods. Depending on the momentum dependence of the
diffusion, additional economies in required spatial and time resolution can be
utilized in the CGMV scheme, as well. These allow a computational speed-up of
at least an order of magnitude in some cases.
