  We develop a new numerical algorithm to model collisional cascades in debris
disks. Because of the large dynamical range in particle masses, we solve the
integro-differential equations describing erosive and catastrophic collisions
in a particle-in-a-box approach, while treating the orbital dynamics of the
particles in an approximate fashion. We employ a new scheme for describing
erosive (cratering) collisions that yields a continuous set of outcomes as a
function of colliding masses. We demonstrate the stability and convergence
characteristics of our algorithm and compare it with other treatments. We show
that incorporating the effects of erosive collisions results in a decay of the
particle distribution that is significantly faster than with purely
catastrophic collisions.
