Approximation of the invariant measure for stochastic Allen-Cahn equation via an explicit fully discrete scheme
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866915946396909568 |
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| author | Wang, Yibo Cao, Wanrong |
| author_facet | Wang, Yibo Cao, Wanrong |
| contents | In this paper we propose an explicit fully discrete scheme to numerically solve the stochastic Allen-Cahn equation. The spatial discretization is done by a spectral Galerkin method, followed by the temporal discretization by a tamed accelerated exponential Euler scheme. Based on the time-independent boundedness of moments of numerical solutions, we present the weak error analysis in an infinite time interval by using Malliavin calculus. This provides a way to numerically approximate the invariant measure for the stochastic Allen-Cahn equation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_00953 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Approximation of the invariant measure for stochastic Allen-Cahn equation via an explicit fully discrete scheme Wang, Yibo Cao, Wanrong Numerical Analysis 60H35, 60H15, 65C30 In this paper we propose an explicit fully discrete scheme to numerically solve the stochastic Allen-Cahn equation. The spatial discretization is done by a spectral Galerkin method, followed by the temporal discretization by a tamed accelerated exponential Euler scheme. Based on the time-independent boundedness of moments of numerical solutions, we present the weak error analysis in an infinite time interval by using Malliavin calculus. This provides a way to numerically approximate the invariant measure for the stochastic Allen-Cahn equation. |
| title | Approximation of the invariant measure for stochastic Allen-Cahn equation via an explicit fully discrete scheme |
| topic | Numerical Analysis 60H35, 60H15, 65C30 |
| url | https://arxiv.org/abs/2408.00953 |