Linearly implicit structure-preserving schemes for Hamiltonian systems
Numerical Analysis
2020-05-11 v3 Numerical Analysis
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.
Keywords
Cite
@article{arxiv.1901.03573,
title = {Linearly implicit structure-preserving schemes for Hamiltonian systems},
author = {Sølve Eidnes and Lu Li and Shun Sato},
journal= {arXiv preprint arXiv:1901.03573},
year = {2020}
}
Comments
18 pages, 11 figures, 33 subfigures. Submitted to Journal of Computational and Applied Mathematics, proceedings for NUMDIFF-15