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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2410.22359 |
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| _version_ | 1866914449429889024 |
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| author | Armstrong-Goodall, Jacob Bruned, Yvain |
| author_facet | Armstrong-Goodall, Jacob Bruned, Yvain |
| contents | We introduce a class of symplectic resonance based schemes for Schrödinger's equation in dimension one, building on the work in [1] wherein resonance based numerical schemes were developed in the context of dispersive PDE driven by time dependent, or space-time dependent, coloured noise. We work primarily with a cubic nonlinearity, advancing the approach introduced in [15] for deriving symplectic schemes in the deterministic setting. As an example of such a scheme we derive the resonance based midpoint rule for the Stochastic NLS and analyse its convergence properties. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_22359 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Low regularity symplectic schemes for stochastic NLS Armstrong-Goodall, Jacob Bruned, Yvain Analysis of PDEs Numerical Analysis Probability 60H15, 65M22 We introduce a class of symplectic resonance based schemes for Schrödinger's equation in dimension one, building on the work in [1] wherein resonance based numerical schemes were developed in the context of dispersive PDE driven by time dependent, or space-time dependent, coloured noise. We work primarily with a cubic nonlinearity, advancing the approach introduced in [15] for deriving symplectic schemes in the deterministic setting. As an example of such a scheme we derive the resonance based midpoint rule for the Stochastic NLS and analyse its convergence properties. |
| title | Low regularity symplectic schemes for stochastic NLS |
| topic | Analysis of PDEs Numerical Analysis Probability 60H15, 65M22 |
| url | https://arxiv.org/abs/2410.22359 |