9 papers · 1 filter
Multi-indice B-series
Yvain Bruned, Kurusch Ebrahimi-Fard, Yingtong Hou
We propose a novel way to study numerical methods for ordinary differential equations in one dimension via the notion of multi-indice. The main idea is to replace rooted trees in B…
Derivation of normal forms for dispersive PDEs via arborification
Yvain Bruned
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 m…
Composition and substitution of Regularity Structures B-series
Yvain Bruned
In this work, we introduce Regularity Structures B-series which are used for describing solutions of singular stochastic partial differential equations (SPDEs). We define compositi…
A top-down approach to algebraic renormalization in regularity structures based on multi-indices
Yvain Bruned, Pablo Linares
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 ``…
Geometric embedding for regularity structures
Yvain Bruned, Foivos Katsetsiadis
In this paper, we show how one can view certain models in regularity structures as some form of geometric rough paths. This is performed by identifying the deformed Butcher-Connes-…
Multi-indices coproducts from ODEs to singular SPDEs
Yvain Bruned, Yingtong Hou
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…