Zobrazeno 1 - 10
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pro vyhledávání: '"Bruned, Yvain"'
Autor:
Bruned, Yvain
In this work, we propose a systematic derivation of normal forms for dispersive equations using decorated trees introduced in arXiv:2005.01649. The key tool is the arborification map which is a morphism from the Butcher-Connes-Kreimer Hopf algebra to
Externí odkaz:
http://arxiv.org/abs/2409.03642
Autor:
Bruned, Yvain, Hou, Yingtong
In this work, we introduce explicit formulae for the coproducts at play for multi-indices in ODEs and in singular SPDEs. The two coproducts described correspond to versions of the Butcher-Connes-Kreimer and extraction/contraction coproducts with mult
Externí odkaz:
http://arxiv.org/abs/2405.11314
Autor:
Bruned, Yvain, Dotsenko, Vladimir
We characterise the chain rule symmetry for the geometric stochastic heat equations in the full subcritical regime for Gaussian and non-Gaussian noises. We show that the renormalised counter-terms that give a solution invariant under changes of coord
Externí odkaz:
http://arxiv.org/abs/2403.17066
We propose a novel way to describe numerical methods for ordinary differential equations via the notion of multi-indice. The main idea is to replace rooted trees in Butcher's B-series by multi-indices. The latter were introduced recently in the conte
Externí odkaz:
http://arxiv.org/abs/2402.13971
We derive the renormalised equation for the quasi-generalised KPZ equation with space-time white noise. We complement the program initiated by Gerencs\'er and Hairer for solving quasi-linear equations using regularity structures by an algebraic machi
Externí odkaz:
http://arxiv.org/abs/2401.13620
Resonance based numerical schemes are those in which cancellations in the oscillatory components of the equation are taken advantage of in order to reduce the regularity required of the initial data to achieve a particular order of error and converge
Externí odkaz:
http://arxiv.org/abs/2312.16690
Autor:
Bruned, Yvain, Dotsenko, Vladimir
In this work, we introduce multi-Novikov algebras, a generalisation of Novikov algebras with several binary operations indexed by a given set, and show that the multi-indices recently introduced in the context of singular stochastic partial different
Externí odkaz:
http://arxiv.org/abs/2311.09091
Autor:
Bruned, Yvain
In this work, we introduce Regularity Structures B-series which are used for describing solutions of singular stochastic partial differential equations (SPDEs). We define composition and substitutions of these B-series and as in the context of B-seri
Externí odkaz:
http://arxiv.org/abs/2310.14242
Autor:
Bruned, Yvain, Linares, Pablo
We provide an algebraic framework to describe renormalization in regularity structures based on multi-indices for a large class of semi-linear stochastic PDEs. This framework is ``top-down", in the sense that we postulate the form of the counterterm
Externí odkaz:
http://arxiv.org/abs/2307.03036
We introduce a unified framework of symmetric resonance based schemes which preserve central symmetries of the underlying PDE. We extend the resonance decorated trees approach introduced in arXiv:2005.01649 to a richer framework by exploring novel wa
Externí odkaz:
http://arxiv.org/abs/2305.16737