303 citations · 399 across the 20 of their papers we have counts for
8 papers · 1 filter
Detecting and determining preserved measures and integrals of birational maps
Elena Celledoni, Charalambos Evripidou, David McLaren +3
In this paper we use the method of discrete Darboux polynomials to calculate preserved measures and integrals of rational maps. The approach is based on the use of cofactors and Da…
Geometric and integrability properties of Kahan's method
Elena Celledoni, David McLaren, Brynjulf Owren +1
Given a quadratic vector field on \mathbb{R}^n possessing a quadratic first integral depending on two of the independent variables, we give a constructive proof that Kahan's discre…
Two classes of quadratic vector fields for which the Kahan discretization is integrable
Elena Celledoni, Robert I. McLachlan, David I. McLaren +2
Applying Kahan's discretization to the reduced Nahm equations, we obtain two classes of integrable mappings.
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…
Volume Preservation by Runge-Kutta Methods
Philipp Bader, David I McLaren, G. R. W. Quispel +1
It is a classical theorem of Liouville that Hamiltonian systems preserve volume in phase space. Any symplectic Runge-Kutta method will respect this property for such systems, but i…
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…
Projection methods and discrete gradient methods for preserving first integrals of ODEs
R. A. Norton, D. I. McLaren, G. R. W. Quispel +2
In this paper we study linear projection methods for approximating the solution and simultaneously preserving first integrals of autonomous ordinary differential equations. We show…
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…