99 citations · 459 across the 24 of their papers we have counts for
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physics.comp-ph2013★ 3 cited
Locally exact modifications of discrete gradient schemes
Jan L. Cieśliński
Locally exact integrators preserve linearization of the original system at every point. We construct energy-preserving locally exact discrete gradient schemes for arbitrary multidi…
physics.comp-ph2010
Discrete gradient algorithms of high order for one-dimensional systems
Jan L. Cieśliński, Bogusław Ratkiewicz
We show how to increase the order of one-dimensional discrete gradient numerical integrator without losing its advantages, such as exceptional stability, exact conservation of the…
physics.comp-ph2008★ 17 cited
Long-time behaviour of discretizations of the simple pendulum equation
J. L. Cieslinski, B. Ratkiewicz
We compare the performance of several discretizations of the simple pendulum equation in a series of numerical experiments. The stress is put on the long-time behaviour. We choose…