Linearly implicit local and global energy-preserving methods for PDEs with a cubic Hamiltonian
Numerical Analysis
2020-07-14 v2 Numerical Analysis
Abstract
We present linearly implicit methods that preserve discrete approximations to local and global energy conservation laws for multi-symplectic PDEs with cubic invariants. The methods are tested on the one-dimensional Korteweg-de Vries equation and the two-dimensional Zakharov-Kuznetsov equation; the numerical simulations confirm the conservative properties of the methods, and demonstrate their good stability properties and superior running speed when compared to fully implicit schemes.
Keywords
Cite
@article{arxiv.1907.02122,
title = {Linearly implicit local and global energy-preserving methods for PDEs with a cubic Hamiltonian},
author = {Sølve Eidnes and Lu Li},
journal= {arXiv preprint arXiv:1907.02122},
year = {2020}
}
Comments
28 pages, 8 figures, 16 subfigures