The Doi-Edwards model is simulated in startup of two-dimensional complex flow. The flow geometry is that of a cylinder confined between two parallel plates. Two different, new simulation methods are used. The first is based on the configuration field approach. The second method is a new method which is introduced in this paper. We refer to this approach as the deformation field method. Theoretically the methods are equivalent. It will be shown that the deformation field approach is very efficient. Furthermore, the method opens up possibilities of studying extensions of the Doi-Edwards model which include tube-stretch and convected constraint release.