5 papers · 1 filter
Backward error analysis for matrix discretizations of 2-D Euler equations
Eugen Bronasco, Klas Modin
We introduce a formalism of Lie--Poisson reduction of Butcher series. The corresponding forest momentum map allows for describing backward error analysis of isospectral symplectic…
Spectral Deferred Corrections in the framework of Runge-Kutta methods
Eugen Bronasco, Joscha Fregin, Daniel Ruprecht +1
We interpret a wide range of flavors of Spectral Deferred Corrections (SDC) as Runge-Kutta methods (RKM). Using Butcher series, we show that the considered class of SDC methods ach…
High order integration of stochastic dynamics on Riemannian manifolds with frozen flow methods
Eugen Bronasco, Adrien Busnot Laurent, Baptiste Huguet
We present a new class of numerical methods for solving stochastic differential equations with additive noise on general Riemannian manifolds with high weak order of accuracy. In o…
Efficient Langevin sampling with position-dependent diffusion
Eugen Bronasco, Benedict Leimkuhler, Dominic Phillips +1
We introduce a numerical method for Brownian dynamics with position dependent diffusion tensor which is second order accurate for sampling the invariant measure while requiring onl…
Hopf algebra structures for the backward error analysis of ergodic stochastic differential equations
Eugen Bronasco, Adrien Laurent
While backward error analysis does not generalise straightforwardly to the strong and weak approximation of stochastic differential equations, it extends for the sampling of ergodi…