128 citations · 592 across the 51 of their papers we have counts for
54 papers
Runge--Kutta methods determined from extended phase space methods for Hamiltonian systems
Robert I McLachlan
We study two existing extended phase space integrators for Hamiltonian systems, the {\em midpoint projection method} and the {\em symmetric projection method}, showing that the fir…
Robust chaos in orientation-reversing and non-invertible two-dimensional piecewise-linear maps
Indranil Ghosh, Robert I. McLachlan, David J. W. Simpson
This paper concerns the two-dimensional border-collision normal form -- a four-parameter family of piecewise-linear maps generalising the Lozi family and relevant to diverse applic…
Birational maps from polarization and the preservation of measure and integrals
Robert I McLachlan, David I McLaren, G R W Quispel
The main result of this paper is the discretization of Hamiltonian systems of the form , where is a constant symmetric matrix and $W\colon\mathbb{R}^n…
The aromatic bicomplex for the description of divergence-free aromatic forms and volume-preserving integrators
Adrien Laurent, Robert I. McLachlan, Hans Z. Munthe-Kaas +1
Aromatic B-series were introduced as an extension of standard Butcher-series for the study of volume-preserving integrators. It was proven with their help that the only volume-pres…
Using aromas to search for preserved measures and integrals in Kahan's method
Geir Bogfjellmo, Elena Celledoni, Robert McLachlan +2
The numerical method of Kahan applied to quadratic differential equations is known to often generate integrable maps in low dimensions and can in more general situations exhibit pr…
Backward error analysis for conjugate symplectic methods
Robert I McLachlan, Christian Offen
The numerical solution of an ordinary differential equation can be interpreted as the exact solution of a nearby modified equation. Investigating the behaviour of numerical solutio…