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Spectral methods for mesoscopic models of pattern formation. (English) Zbl 0987.65007
Summary: 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.

MSC:
65C30 Numerical solutions to stochastic differential and integral equations
82C22 Interacting particle systems in time-dependent statistical mechanics
82C80 Numerical methods of time-dependent statistical mechanics (MSC2010)
60H20 Stochastic integral equations
45K05 Integro-partial differential equations
65R30 Numerical methods for ill-posed problems for integral equations
60H35 Computational methods for stochastic equations (aspects of stochastic analysis)
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