Abstract
Techniques from numerical bifurcation theory are very useful to studytransitions between steady fluid flow patterns and the instabilities involved.Here, we provide computational methodology to use parameter continuationin determining probability density functions of systems of stochasticpartial differential equations near fixed points, under a small noise approximation.Key innovation is the efficient solution of a generalized Lyapunovequation using an iterative method involving low-rank approximations. Weapply and illustrate the capabilities of the method using a problem inphysical oceanography, i.e. the occurrence of multiple steady states of theAtlantic Ocean circulation
Original language | English |
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Pages (from-to) | 627-643 |
Number of pages | 31 |
Journal | Journal of computational physics |
Volume | 336 |
DOIs | |
Publication status | Published - 1-May-2017 |
Keywords
- continuation of fixed points
- stochastic dynamical systems
- Lyapunov equation
- probability density function
- RATIONAL KRYLOV SUBSPACES
- DYNAMICAL-SYSTEMS
- EQUATIONS
- ALGORITHM
- MODELS