We perform a numerical analysis of randomly perturbed Poisson systems } } . For the considered It\^o perturbation of Poisson differential equations , we show the longtime behavior of the energy and quadratic Casimirs for the exact solution. We then propose and analyze a drift-preserving splitting scheme for such problems with the following properties: exact drift preservation of energy and quadratic Casimirs, mean-square order of convergence one, weak order of convergence two. Finally, extensive numerical experimentsillustrate the performance of the proposed numerical scheme .
We perform a numerical analysis of a class of randomly perturbed H}amiltonian systems and P}oisson systems . For the considered additive noise perturbation of such systems , we show the long time behavior of the energy and quadratic Casimirs for the exact solution. We then propose and analyze a drift-preserving splitting scheme for such problems with the following properties: exact drift preservation of energy and quadratic Casimirs, mean-square order of convergence one, weak order of convergence two. These properties are illustrated with numerical experiments .
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randomly perturbed Poisson systems
a class of randomly perturbed
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H
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amiltonian systems and
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P
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oisson systems
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It\^o perturbation of Poisson differential equations
additive noise perturbation of such systems
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longtime
long time
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Finally, extensive numerical experimentsillustrate the performance of the proposed numerical scheme
These properties are illustrated with numerical experiments