Team
IPSO

Overall Objectives

Scientific Foundations

Application Domains

New Results

- A Fast Multipole Method for Geometric Numerical Integrations of Hamiltonian Systems
- Composing B-series of integrators and vector fields
- Resonances in long time integration of semi-linear Hamiltonian PDEs.
- Quasi invariant modified Sobolev norms for semi-linear reversible PDEs.
- Modified energy for split-step methods applied to the linear Schrödinger equation.
- Birkhoff normal form for splitting methods applied semi linear Hamiltonian PDEs. Part II: Abstract splitting
- A probabilistic approach of high-dimensional least-squares approximations
- Computing semi-classical quantum dynamics with Hagedorn wavepackets
- Conservative stochastic differential equations: Mathematical and numerical analysis
- Analysis of splitting methods for reaction-diffusion problems using stochastic calculus
- Weak approximation of stochastic partial differential equations: the nonlinear case
- Long-time behavior in scalar conservation laws
- Soliton dynamics for the Korteweg-de Vries equation with multiplicative homogeneous noise
- Weak order for the discretization of the stochastic heat equation
- Hybrid stochastic simplifications for multiscale gene networks
- Moments analysis in Markov reward models.
- The strongly confined Schrödinger-Poisson system for the transport of electrons in a nanowire.
- An averaging technique for highly-oscillatory Hamiltonian problems.
- Propagation of Gevrey regularity over long times for the fully discrete Lie Trotter splitting scheme applied to the linear Schrödinger equation.
- Splitting methods with complex times for parabolic equations
- Higher-order averaging, formal series and numerical integration
- An algebraic theory of order

Other Grants and Activities

Dissemination

Bibliography