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Linearly implicit structure-preserving schemes for Hamiltonian systems (1901.03573v3)
Published 11 Jan 2019 in math.NA and cs.NA
Abstract: Kahan's method and a two-step generalization of the discrete gradient method are both linearly implicit methods that can preserve a modified energy for Hamiltonian systems with a cubic Hamiltonian. These methods are here investigated and compared. The schemes are applied to the Korteweg-de Vries equation and the Camassa-Holm equation, and the numerical results are presented and analysed.