Numerical computation of sharp travelling waves of a degenerate diffusion–reaction equation arising in biofilm modelling

•A numerical method for travelling waves of degenerate diffusion–reaction equations with gradient blow-up at the wave front.•The underlying idea is to approximate the double degenerate problem by a sequence of single degenerate problems.•The wave speed of the original problem is found as the limit of the wave speed of these auxiliary problems.•The method is tested on a model that arises in the study of bacterial biofilms.