Recently the leptonic component of the cosmic ray spectrum has gained new attention. New observations from ATIC, PAMELA and Fermi show a deviation from a power-law in the form of an excess in both the electron and positron spectra. Annihilating dark matter and nearby pulsars (among other things) have been proposed as possible sources of the excess leptons. Regardless of the source, a new propagation model is needed to connect the energy spectrum measured on earth with the injection spectra.

We present our numerical cosmic ray transport model in application to the high energy electron transport in the ISM. Spatial and momentum diffusion, particle escape, acceleration via Fermi I and continuous energy losses were taken into account and their effects on the steady-state energy spectrum analyzed. In solving the transport equation we employed quasi-linear transport theory, the diffusion approximation and a separation of the spatial and momentum problem to obtain the leaky-box-equation, which was then solved numerically. The spatial problem was solved analytically in cylindrical and prolate spheroidal coordinates. We found that despite the many simplifications we are able to reproduce the general shape of the high energy electron spectrum.