PSEUDOSPECTRAL METHODS AND LINEAR INSTABILITIES IN REACTION-DIFFUSIONFRONTS

We explore the application of a pseudo-spectral Fourier method to a se t of reaction-diffusion equations and compare it with a second-order f inite difference method. The prototype cubic autocatalytic reaction-di ffusion model as discussed by Gray and Scott [Chem. Eng. Sci. 42, 307 (1987)] with a nonequilibrium constraint is adopted. In a spatial reso lution study we find that the phase speeds of one-dimensional finite a mplitude waves converge more rapidly for the spectral method than for the finite difference method. Furthermore, in two dimensions the symme try preserving properties of the spectral method are shown to be super ior to those of the finite difference method. In studies of plane/axis ymmetric nonlinear waves a symmetry breaking linear instability is sho wn to occur and is one possible route for the formation of patterns fr om infinitesimal perturbations to finite amplitude waves in this set o f reaction-diffusion equations. (C) 1996 American Institute of Physics .