Spectral methods for mesoscopic models of pattern formation

In this paper we present spectral algorithms for the solution of mesoscopic equations describing a broad class of pattern formation mechanisms, focusi ng oil a prototypical system of surface processes. These models are in prin ciple stochastic integrodifferential equations and are derived directly fro m microscopic lattice models, containing detailed information on particle-p article interactions and particle dynamics. The enhanced computational effi ciency and accuracy of spectral methods versus finite difference methods ar e also described. (C) 2001 Academic Press.