AN EXPLICIT SUBPARAMETRIC SPECTRAL ELEMENT METHOD OF LINES APPLIED TO A TUMOUR ANGIOGENESIS SYSTEM OF PARTIAL DIFFERENTIAL EQUATIONS

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