Splitting integrators for linear Vlasov equations with stochastic perturbations
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866913248060637184 |
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| author | Bréhier, Charles-Edouard Cohen, David |
| author_facet | Bréhier, Charles-Edouard Cohen, David |
| contents | We consider a class of linear Vlasov partial differential equations driven by Wiener noise. Different types of stochastic perturbations are treated: additive noise, multiplicative Itô and Stratonovich noise, and transport noise. We propose to employ splitting integrators for the temporal discretization of these stochastic partial differential equations. These integrators are designed in order to preserve qualitative properties of the exact solutions depending on the stochastic perturbation, such as preservation of norms or positivity of the solutions. We provide numerical experiments in order to illustrate the properties of the proposed integrators and investigate mean-square rates of convergence. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_18982 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Splitting integrators for linear Vlasov equations with stochastic perturbations Bréhier, Charles-Edouard Cohen, David Numerical Analysis Probability We consider a class of linear Vlasov partial differential equations driven by Wiener noise. Different types of stochastic perturbations are treated: additive noise, multiplicative Itô and Stratonovich noise, and transport noise. We propose to employ splitting integrators for the temporal discretization of these stochastic partial differential equations. These integrators are designed in order to preserve qualitative properties of the exact solutions depending on the stochastic perturbation, such as preservation of norms or positivity of the solutions. We provide numerical experiments in order to illustrate the properties of the proposed integrators and investigate mean-square rates of convergence. |
| title | Splitting integrators for linear Vlasov equations with stochastic perturbations |
| topic | Numerical Analysis Probability |
| url | https://arxiv.org/abs/2402.18982 |