596 citations
- University of AucklandNZ188 papers
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Showing 1998Show all
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math.NA1998
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…
math.NA1998★ 1 cited
Spatial discretization of partial differential equations with integrals
Robert I McLachlan
We consider the problem of constructing spatial finite difference approximations on a fixed, arbitrary grid, which have analogues of any number of integrals of the partial differen…
math-ph1998★ 103 cited
A unified approach to Hamiltonian systems, Poisson systems, gradient systems, and systems with Lyapunov functions and/or first integrals
Robert I McLachlan, GRW Quispel, Nicolas Robidoux
Systems with a first integral (i.e., constant of motion) or a Lyapunov function can be written as ``linear-gradient systems'' for an appropriate matrix fu…