Linearly implicit structure-preserving schemes for Hamiltonian systems
arXiv:1901.03573
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.
18 pages, 11 figures, 33 subfigures. Submitted to Journal of Computational and Applied Mathematics, proceedings for NUMDIFF-15