Simulations of Ultra High Energy Cosmic Rays propagation
  We compare two techniques for simulation of Ultra High Energy Cosmic Rays (UHECR) propagation, the Monte Carlo approach and method based on solving transport equations in one dimension. For the former we adopt publicly available tool CRPropa and for the later we use the code TransportCR developed by O.K. et al. and used in number of applications which is made available online with publishing this paper. While the CRPropa code is more universal, transport equation solver has advantage of roughly 100 times higher calculation speed. We conclude that the methods give practically identical results for the case of proton or neutron primaries provided that some accuracy improvements are introduced to CRPropa code. 
O. E. Kalashev and E. Kido
astro-ph.HE