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Some perturbations of discrete nature are known to influence the performance of a proton storage ring, contributing to parasitic background, decay of beam currents and bunch tail buildup. Such are, for example, intra-beam scattering and residual gas scattering .These processes are to a big extent described by existing analytical theory. The latter, employing a large amount of averaging, usually neglects effects arising from system nonlinearity. So, the motion of tail particles in the presence of a sufficiently nonlinear RF voltage under influence of intra-beam scattering strongly deviates from the average across the bunch and the analytical approach seems inadequate for it. To overcome this situation we have developed more accurate numerical methods for calculations of bunch evolution under influence of a rather broad class of jump-like perturbations. Here we present the computational algorithms and their application to assessment of coasting beam and proton background in HERA-p.
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