Copyright © 2011 M. Kolev and B. Zubik-Kowal. This is an open access article distributed under the
Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
The goal of this paper is to construct a new algorithm for the numerical simulations of the evolution of tumour invasion and metastasis.
By means of mathematical model equations and their numerical solutions we investigate how cancer cells can produce and secrete matrix
degradative enzymes, degrade extracellular matrix, and invade due to diffusion and haptotactic migration. For the numerical simulations
of the interactions between the tumour cells and the surrounding tissue, we apply numerical approximations, which are spectrally accurate
and based on small amounts of grid-points. Our numerical experiments illustrate the metastatic ability of tumour cells.