Wiener chaos vs stochastic collocation methods for linear advection-diffusion equations with multiplicative white noise
SIAM J. Numer. Anal., 53(1): 153-183, 2015 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...
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Main Authors | , , , |
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Format | Journal Article |
Language | English |
Published |
14.05.2015
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Subjects | |
Online Access | Get full text |
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Summary: | SIAM J. Numer. Anal., 53(1): 153-183, 2015 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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DOI: | 10.48550/arxiv.1505.03771 |