128 citations · 592 across the 51 of their papers we have counts for
4 papers · 1 filter
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…
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}^{…
Modified trigonometric integrators
Robert I. McLachlan, Ari Stern
We study modified trigonometric integrators, which generalize the popular class of trigonometric integrators for highly oscillatory Hamiltonian systems by allowing the fast frequen…
Discrete gradient methods have an energy conservation law
Robert I McLachlan, G R W Quispel
We show for a variety of classes of conservative PDEs that discrete gradient methods designed to have a conserved quantity (here called energy) also have a time-discrete conservati…