303 citations · 457 across the 7 of their papers we have counts for
4 papers · 1 filter
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…
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…