  In this manuscript we present a new approach for the numerical solution of
the Galactic Cosmic Ray propagation problem. We introduce a method using
advanced contemporary numerical algorithms while retaining the general
complexity of other established codes. In this paper we present the underlying
numerical scheme in conjunction with tests showing the correctness of the
scheme. Finally we show the solution of a first example propagation problem
using the new code to show its applicability to Galactic Cosmic Ray
propagation.

High Energy Astrophysical Phenomena