39 citations · 312 across the 32 of their papers we have counts for
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math.NA2013★ 6 cited
Collective symplectic integrators
Robert I McLachlan, Klas Modin, Olivier Verdier
We construct symplectic integrators for Lie-Poisson systems. The integrators are standard symplectic (partitioned) Runge--Kutta methods. Their phase space is a symplectic vector sp…
math.NA2013★ 30 cited
Aromatic Butcher Series
Hans Munthe-Kaas, Olivier Verdier
We show that without other further assumption than affine equivariance and locality, a numerical integrator has an expansion in a generalized form of Butcher series (B-series) whic…
math.NA2013★ 17 cited
Collective Lie-Poisson integrators on
Robert McLachlan, Klas Modin, Olivier Verdier
We develop Lie-Poisson integrators for general Hamiltonian systems on equipped with the rigid body bracket. The method uses symplectic realisation of $\mathbf{R}^{…