English

Metastable energy strata in numerical discretizations of weakly nonlinear wave equations

Numerical Analysis 2016-12-22 v2

Abstract

The quadratic nonlinear wave equation on a one-dimensional torus with small initial values located in a single Fourier mode is considered. In this situation, the formation of metastable energy strata has recently been described and their long-time stability has been shown. The topic of the present paper is the correct reproduction of these metastable energy strata by a numerical method. For symplectic trigonometric integrators applied to the equation, it is shown that these energy strata are reproduced even on long time intervals in a qualitatively correct way.

Keywords

Cite

@article{arxiv.1606.00647,
  title  = {Metastable energy strata in numerical discretizations of weakly nonlinear wave equations},
  author = {Ludwig Gauckler and Daniel Weiss},
  journal= {arXiv preprint arXiv:1606.00647},
  year   = {2016}
}

Comments

28 pages, 9 figures