129 citations · 316 across the 45 of their papers we have counts for
8 papers · 1 filter
Derivation of resonance-based schemes via normal forms
Yvain Bruned
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 Butch…
Elementary differentials from multi-indices to rooted trees
Yvain Bruned, Paul Laubie
Rooted trees are essential for describing numerical schemes via the so-called B-series. They have also been used extensively in rough analysis for expanding solutions of singular S…
Resonances and computations
Yvain Bruned, Frédéric Rousset, Katharina Schratz
The computation of time dynamics arising in nonlinear time-dependent partial differential equations is an ongoing challenge in numerical analysis, especially once roughness comes i…
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…
Resonance based schemes for SPDEs
Jacob Armstrong-Goodall, Yvain Bruned
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 o…
Symmetric resonance based integrators and forest formulae
Yvonne Alama Bronsard, Yvain Bruned, Georg Maierhofer +1
In the present work we introduce a unified framework that allows for the very first systematic construction of symmetric resonance-based integrators to approximate a wide class of…
Low regularity integrators via decorated trees
Yvonne Alama Bronsard, Yvain Bruned, Katharina Schratz
We introduce a general framework of low regularity integrators which allows us to approximate the time dynamics of a large class of equations, including parabolic and hyperbolic pr…
Resonance based schemes for dispersive equations via decorated trees
Yvain Bruned, Katharina Schratz
We introduce a numerical framework for dispersive equations embedding their underlying resonance structure into the discretisation. This will allow us to resolve the nonlinear osci…