In this paper, we present a new approach to the deformation fields method that has recently been introduced to solve integral type models in complex flows (E.A.J.F. Peters, M.A. Hulsen, B.H.A.A. van den Brule, J. Non-Newtonian fluid Mechanics 89 (2000) 209-228). The new approach is based on a change of the reference time of the fields from an absolute time to a time relative to the current time. This basically removes most, if not all, stability and accuracy problems that exist in the original method compared to using differential models. Also the new implementation is much more flexible with respect to the time integral discretisation, opening the way to adaptive refinement. The new implementation has been tested for two problems: the standard 2:1 benchmark of a the flow around a sphere using a UCM model and the flow around a sphere in a different geometry using a PSM model.