Summary: A new method for solving the Boltzmann transport equation is introduced. The method is based on a discontinuous spline approximation of the distribution function in the whole phase space. This procedure enables us to avoid the widely used \(P_N\)-approximation for the angle dependence of the distribution function, so that we are able to treat strong anisotropies. The method is applied to a nonparabolic multivalley model of silicon, which allows for the investigation of the anisotropic high field transport of electrons in \(n\)-type silicon. The results are compared to experimental data and Monte Carlo simulations.