  We construct an algorithm for approximating the invariant tori created at a
Neimark-Sacker bifurcation point. It is based on the same philosophy as many
algorithms for approximating the periodic orbits created at a Hopf bifurcation
point, i.e. a Fourier spectral method. For Neimark-Sacker bifurcation, however,
we use a simple parametrisation of the tori in order to determine low-order
approximations, and then utilise the information contained therein to develop a
more general parametrisation suitable for computing higher-order
approximations. Different algorithms, applicable to either autonomous or
periodically-forced systems of differential equations, are obtained.
