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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).…
math.NA2009★ 26 cited
How to improve the accuracy of the discrete gradient method in the one-dimensional case
Jan L. Cieslinski, Boguslaw Ratkiewicz
We present a new numerical scheme for one dimensional dynamical systems. This is a modification of the discrete gradient method and keeps its advantages, including the stability an…