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We derive a general renormalized potential-following propagation method that efficiently solves the coupled-channels equations. The step size is variable, the method is compatible with reactive boundary conditions, and the algorithm may be combined with other renormalized algorithms, such as renormalized Numerov. We diagonalize the coupling matrix and consider piece-wise constant and linear reference potentials. The constant reference potential algorithm is very simple to implement, yet for multichannel problems almost as accurate as the linear reference potential method. The applicability of the proposed algorithms to realistic problems is demonstrated for cold collisions of NH radicals. The renormalized approach has the advantage of producing wave functions in a straightforward way, which is illustrated for a shape resonance in NH-NH collisions. These scattering wave functions can be used to study ultracold photoassociation and near-threshold photodissociation.

A renormalized potential-following propagation algorithm for solving the coupled-channels equations