Structure-preserving finite difference schemes for nonlinear wave equations with dynamic boundary conditions
Numerical Analysis
2021-12-14 v1 Numerical Analysis
Analysis of PDEs
Abstract
In this article we discuss the numerical analysis for the finite difference scheme of the one-dimensional nonlinear wave equations with dynamic boundary conditions. From the viewpoint of the discrete variational derivative method we propose the derivation of the structure-preserving finite difference schemes of the problem which covers a variety of equations as widely as possible. Next, we focus our attention on the semilinear wave equation, and show the existence and uniqueness of solution for the scheme and error estimates with the help of the inherited energy structure.
Keywords
Cite
@article{arxiv.2104.00398,
title = {Structure-preserving finite difference schemes for nonlinear wave equations with dynamic boundary conditions},
author = {Akihiro Umeda and Yuta Wakasugi and Shuji Yoshikawa},
journal= {arXiv preprint arXiv:2104.00398},
year = {2021}
}
Comments
27 pages, 5 figures