Solving the cosmic-ray transport equation with stochastic differential equations: CRPropa's module DiffusionSDE

An appropriate numerical modelling of Galactic cosmic-ray transport is a major challenge in modern astroparticle physics. Multi-messenger observations of cosmic rays and neutral secondary particles like neutrinos and gamma-rays must be connected with source models. This requires a detailed description of the propagation and interaction of all particles. Over the years many different approaches to describe the Galactic cosmic-ray transport have been developed. From early semi-analytical simplifications to modern simulations frameworks a lot of progress has been made, e.g. the introduction of three-dimensional diffusion in recent tools. Furthermore, new solver techniques for the transport equation based on stochastic differential equations have become available e.g. in CRPropa. In this talk the differences compared with conventional grid-based solvers are explained. In addition, it is shown why this ansatz is especially promising in the shin region between the cosmic-ray knee and ankle.