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, focusing on a prototypical system of surface processes. These models are in principle stochastic integrodifferential equations and are derived directly from microscopic lattice models, containing detailed information on particle–particle interactions and particle dynamics. The enhanced computational efficiency and accuracy of spectral methods versus finite difference methods are also described.