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|Title:||Computer algebra compares the stochastic superslow manifold of an averaged SPDE with that of the original slow-fast SPDE|
|Roberts, A. J.|
|Abstract:||The computer algebra routines documented here empower you to reproduce and check many of the details described by an article on large deviations for slow-fast stochastic systems [Wang et al., 2010]. We consider a `small' spatial domain with two coupled concentration fields, one governed by a `slow' reaction-diffusion equation and one governed by a stochastic `fast' linear equation. In the regime of a stochastic bifurcation, we derive two superslow models of the dynamics: the first is of the averaged model of the slow dynamics derived via large deviation principles; and the second is of the original fast-slow dynamics. Comparing the two superslow models validates the averaging in the large deviation principle in this parameter regime|
|Keywords:||Computer algebra; stochastic partial differential equations; stochastic centre manifold; slow-fast systems; large deviations|
|Appears in Collections:||Applied Mathematics publications|
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