Numeric solution of cascade equations for fast high-energy air shower simulation

The processes in cosmic ray induced air showers can be described by cascade equations. These are systems of coupled partial differential equations. In the current work we present a scheme for the numeric solution of the electromagnetic cascade equations. Our purpose is to speed up the treatment of the electromagnetic component in hybrid air shower simulations. The numerical results are verified by comparisons with independent Monte Carlo simulations and the historical approximations A and B. Then the numerical method and the Monte Carlo simulation are combined into a hybrid simulation scheme. Finally we compare the numerical results to CORSIKA simulations, analyze two Auger events and investigate the calculation times and accuracy of the numerical method. (orig.)