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Computational Schemes for the Propagation of Ultra High Energy Cosmic Rays

We discuss the problem of ultra high energy particles propagation in astrophysical backgrounds. We present two different computational schemes based on both kinetic and Monte Carlo approaches. The kinetic approach is an analytical computation scheme based on the hypothesis of continuos energy losses while the Monte Carlo scheme takes into account also the stochastic nature of particle interactions. These schemes, that give quite reliable results, enable the computation of fluxes keeping track of the different primary and secondary components, providing a fast and useful workbench to study Ultra High Energy Cosmic Rays.