Derivation of resonance-based schemes via normal forms
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866917072943972352 |
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| author | Bruned, Yvain |
| author_facet | Bruned, Yvain |
| contents | In this work, we propose a systematic derivation of resonance-based schemes via normal forms. The main idea is to use an arborification map on decorated trees together with a Butcher-Connes-Kreimer type coproduct and lower-dominant parts decompositions of the Fourier operator coming from the nonlinear interactions. This new family of low regularity schemes has explicit formulae for its coefficients and its local error. Under a mild assumption, one could expect these schemes to have a similar local error as the low regularity schemes proposed in arXiv:2005.01649. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_07838 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Derivation of resonance-based schemes via normal forms Bruned, Yvain Numerical Analysis Analysis of PDEs Rings and Algebras In this work, we propose a systematic derivation of resonance-based schemes via normal forms. The main idea is to use an arborification map on decorated trees together with a Butcher-Connes-Kreimer type coproduct and lower-dominant parts decompositions of the Fourier operator coming from the nonlinear interactions. This new family of low regularity schemes has explicit formulae for its coefficients and its local error. Under a mild assumption, one could expect these schemes to have a similar local error as the low regularity schemes proposed in arXiv:2005.01649. |
| title | Derivation of resonance-based schemes via normal forms |
| topic | Numerical Analysis Analysis of PDEs Rings and Algebras |
| url | https://arxiv.org/abs/2511.07838 |