53 citations · 187 across the 29 of their papers we have counts for
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Analogues of Kahan's method for higher order equations of higher degree
A. N. W. Hone, G. R. W. Quispel
Kahan introduced an explicit method of discretization for systems of first order differential equations with nonlinearities of degree at most two (quadratic vector fields). Kahan's…
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…
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…
Symmetric spaces and Lie triple systems in numerical analysis of differential equations
Hans Z. Munthe-Kaas, Gilles Reinout W. Quispel, Antonella Zanna
A remarkable number of different numerical algorithms can be understood and analyzed using the concepts of symmetric spaces and Lie triple systems, which are well known in differen…