303 citations · 457 across the 7 of their papers we have counts for
7 papers
Measure preservation and integrals for Lotka--Volterra tree-systems and their Kahan discretisation
Peter H. van der Kamp, Robert I. McLachlan, David I. McLaren +1
We show that any Lotka--Volterra tree-system associated with an -vertex tree, as introduced in Quispel et al., J. Phys. A 56 (2023) 315201, preserves a rational measure. We also…
The use of discrete gradient methods for total variation type regularization problems in image processing
V Grimm, R I McLachlan, D McLaren +2
Discrete gradient methods are well-known methods of Geometric Numerical Integration, which preserve the dissipation of gradient systems. The preservation of the dissipation of a sy…
Efficient and accurate methods for solving the time-dependent spin-1 Gross-Pitaevskii equation
L. M. Symes, R. I. McLachlan, P. B. Blakie
We develop a numerical method for solving the spin-1 Gross-Pitaevskii equation. The basis of our work is a two-way splitting of the spin-1 evolution equation that leads to two exac…
Integrability properties of Kahan's method
Elena Celledoni, Robert I McLachlan, David I McLaren +2
We present several novel examples of integrable quadratic vector fields for which Kahan's discretization method preserves integrability. Our examples include generalized Suslov and…
Geometric properties of Kahan's method
Elena Celledoni, Robert I McLachlan, Brynjulf Owren +1
We show that Kahan's discretization of quadratic vector fields is equivalent to a Runge--Kutta method. When the vector field is Hamiltonian on either a symplectic vector space or a…
Preserving energy resp. dissipation in numerical PDEs using the "Average Vector Field" method
E. Celledoni, V. Grimm, R. I. McLachlan +4
We give a systematic method for discretizing Hamiltonian partial differential equations (PDEs) with constant symplectic structure, while preserving their energy exactly. The same m…
Numerical integrators that contract volume
Robert I McLachlan, G R W Quispel
We study numerical integrators that contract phase space volume even when the ODE does so at an arbitrarily small rate. This is done by a splitting into two-dimensional contractive…