Linearly implicit structure-preserving schemes for Hamiltonian systems

Kahan's method and a two-step generalisation 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. (C) 2019 Elsevier B.V. All rights reserved.

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The study investigates and compares Kahan's method and a two-step generalisation of the discrete gradient method, applied to the Korteweg-de Vries equation and the Camassa-Holm equation. Numerical results are presented and analysed in this investigation.