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Methods of modelling curves with both constant and variable radii of curvature are investigated using the finite difference-beam propagation method (FD-BPM). The practical advantages of a cylindrical co-ordinate scheme over a conformally mapped rectangular scheme are clearly demonstrated, the latter possessing a zero order limit on accuracy. A structure-related, FD-BPM scheme is presented for the first time that allows non-uniformly curved waveguide bends to be modelled with the same computational accuracy as their uniformly curved counterparts. This scheme is very flexible and practically reduces the computational resource requirements, thus allowing more complex devices to be completely modelled.