English

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