27 citations · 70 across the 4 of their papers we have counts for
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math.NA2010★ 27 cited
Energy-preserving numerical schemes of high accuracy for one-dimensional Hamiltonian systems
Jan L. Cieśliński, Bogusław Ratkiewicz
We present a class of non-standard numerical schemes which are modifications of the discrete gradient method. They preserve the energy integral exactly (up to the round-off error).…
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…