Wiener chaos vs stochastic collocation methods for linear advection-diffusion equations with multiplicative white noise
We compare Wiener chaos and stochastic collocation methods for linear advection-reaction-diffusion equations with multiplicative white noise. Both methods are constructed based on a recursive multi-stage algorithm for long-time integration. We derive error estimates for both methods and compare thei...
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Published in | arXiv.org |
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Main Authors | , , , |
Format | Paper |
Language | English |
Published |
Ithaca
Cornell University Library, arXiv.org
14.05.2015
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Subjects | |
Online Access | Get full text |
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Summary: | We compare Wiener chaos and stochastic collocation methods for linear advection-reaction-diffusion equations with multiplicative white noise. Both methods are constructed based on a recursive multi-stage algorithm for long-time integration. We derive error estimates for both methods and compare their numerical performance. Numerical results confirm that the recursive multi-stage stochastic collocation method is of order \(\Delta\) (time step size) in the second-order moments while the recursive multi-stage Wiener chaos method is of order \(\Delta^{\mathsf{N}}+\Delta^2\) (\(\mathsf{N}\) is the order of Wiener chaos) for advection-diffusion-reaction equations with commutative noises, in agreement with the theoretical error estimates. However, for non-commutative noises, both methods are of order one in the second-order moments. |
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ISSN: | 2331-8422 |