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Type: Report
Title: Computer algebra compares the stochastic superslow manifold of an averaged SPDE with that of the original slow-fast SPDE
Author: Roberts, A.
Issue Date: 2010
Statement of
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
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Appears in Collections:Applied Mathematics publications
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