In this paper we consider a numerical solution to Anderson and Chaplain's tumour angiogenesis model1 over two-dimensional complex geometry. The numerical solution of the governing system of non-linear evolutionary partial differential equations is obtained using the method of lines: after a spatial semi-discretisation based on the subparametric Legendre spectral element method is performed, the original system of partial differential equations is replaced by an augmented system of stiff ordinary differential equations in autonomous form, which is then advanced forward in time using an explicit time integrator based on the fourth-order Chebyshev polynomial. Numerical simulations show the convergence of the steady state numerical solution towards the linearly stable steady state analytical solution.
|Number of pages
|Mathematical Models and Methods in Applied Sciences
|Published - 2004
- Tumour angiogenesis
- Spectral elements