128 citations · 592 across the 51 of their papers we have counts for
6 papers · 1 filter
Symplectic integration of PDEs using Clebsch variables
Robert I McLachlan, Christian Offen, Benjamin K Tapley
Many PDEs (Burgers' equation, KdV, Camassa-Holm, Euler's fluid equations,...) can be formulated as infinite-dimensional Lie-Poisson systems. These are Hamiltonian systems on manifo…
Three classes of quadratic vector fields for which the Kahan discretization is the root of a generalised Manin transformation
Peter H. van der Kamp, Elena Celledoni, Robert I. McLachlan +3
We apply Kahan's discretisation method to three classes of 2-dimensional quadratic vector fields with quadratic, resp cubic, resp quartic Hamiltonians. We show that the maps obtain…
Symplectic integration of boundary value problems
Robert I McLachlan, Christian Offen
Symplectic integrators can be excellent for Hamiltonian initial value problems. Reasons for this include their preservation of invariant sets like tori, good energy behaviour, none…
Hamiltonian boundary value problems, conformal symplectic symmetries, and conjugate loci
Robert I McLachlan, Christian Offen
In this paper we continue our study of bifurcations of solutions of boundary-value problems for symplectic maps arising as Hamiltonian diffeomorphisms. These have been shown to be…
Preservation of bifurcations of Hamiltonian boundary value problems under discretisation
Robert I McLachlan, Christian Offen
We show that symplectic integrators preserve bifurcations of Hamiltonian boundary value problems and that nonsymplectic integrators do not. We provide a universal description of th…
Parallelisation, initialisation, and boundary treatments for the diamond scheme
Stephen R Marsland, Robert I McLachlan, Matthew C Wilkins
We study a class of general purpose linear multisymplectic integrators for Hamiltonian wave equations based on a diamond-shaped mesh. On each diamond, the PDE is discretized by a s…