In 1999, Ottinger introduced a thermodynamically admissible reptation model incorporating chain stretching, anisotropic tube cross sections, double reptation, and the convective constraint release mechanism. In this paper, we describe and use a new high-order Fokker-Planck-based numerical method for the simulation of the Ottinger model in complex geometries. Evidence, in the case of startup homogeneous flows, of the significant CPU time advantage (for comparable levels of accuracy) of our method over a stochastic simulation [Fang et at. (2000)], is presented. For the confined cylinder benchmark problem, differences in the drag behavior observed between the Ottinger model and those of Doi and Edwards (1978a, 1978b, 1978c) and Mead et al. (1998) are explained in terms of double reptation and the differing relaxation spectra. (C) 2003 The Society of Rheology.