Numerical simulation of pattern formation on surfaces
by
M. Ganesh
University of New South Wales, Sydney
Coauthors: M.A.J. Chaplain (University of Dundee, U.K.), I.G. Graham (University of Bath, U.K.)

In this talk we examine spatio-temporal pattern formation in reaction-diffusion systems on the surface on the sphere in three dimensions. Our numerical scheme is based on the spectral method of lines and uses fast Fourier transforms to expedite the computation of the reaction kinetics. Numerical experiments demonstrate that our method efficiently computes the evolution of spatial patterns and yields numerical results which coincide with those predicted by linear stability analysis. We also investigate the role that pre-pattern (Turing) theory may play in the growth and development of solid tumours.

http://www.maths.unsw.edu.au/~ganesh

Date received: July 8, 1999