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We present a novel numerical model for the propagation of ultra-high energy charged particles in the intergalactic medium, assumed to have a cellular structure of coherent magnetic fields. We take into account the diffusion of ultrarelativistic particles under the influence of the extragalactic magnetic fields and their energy losses. The fields are considered to have random orientations of their vector components within the cells with smooth transitions between them. The propagator presents a very high accuracy on calculating the particle tracking, on the order of $\lesssim 10^{-33}$ of relative error in energy, and $10^{-5}$ in Larmor radius.

A Numerical Model for the Propagation of Ultra-High Energy Cosmic Rays through Extragalactic Magnetic Fields