  A novel numerical technique has been proposed to solve a two-phase tumour
growth model in one spatial dimension without needing to account for the
boundary dynamics explicitly. The equivalence to the standard definition of a
weak solution is proved. The method is tested against equations with
analytically known solutions, to illustrate the advantages over the existing
techniques. The tumour growth model is solved using the new procedure and
showed to be consistent with results available in the literature.
