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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.

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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