128 citations · 592 across the 51 of their papers we have counts for
5 papers · 1 filter
Symmetry reduction for central force problems
Robert I McLachlan, Klas Modin, Olivier Verdier
We given an elementary illustration of symmetry reduction for central force problems, drawing phase portraits of the reduced dynamics as the intersection of Casimir and energy leve…
Butcher series: A story of rooted trees and numerical methods for evolution equations
Robert I McLachlan, Klas Modin, Hans Munthe-Kaas +1
Butcher series appear when Runge-Kutta methods for ordinary differential equations are expanded in power series of the step size parameter. Each term in a Butcher series consists o…
Travelling wave solutions of multisymplectic discretizations of semi-linear wave equations
Fleur McDonald, Robert I McLachlan, Brian E Moore +1
How well do multisymplectic discretisations preserve travelling wave solutions? To answer this question, the 5-point central difference scheme is applied to the semi-linear wave eq…
Discretization of polynomial vector fields by polarization
Elena Celledoni, Robert I. McLachlan, David I. McLaren +2
A novel integration method for quadratic vector fields was introduced by Kahan in 1993. Subsequently, it was shown that Kahan's method preserves a (modified) measure and energy whe…
Geometry of discrete-time spin systems
Robert I. McLachlan, Klas Modin, Olivier Verdier
Classical Hamiltonian spin systems are continuous dynamical systems on the symplectic phase space . In this paper we investigate the underlying geometry of a time discreti…