Error estimates for Euler discretization of high-index saddle dynamics
Numerical Analysis
2022-08-05 v2 Numerical Analysis
Abstract
High-index saddle dynamics provides an effective means to compute the any-index saddle points and construct the solution landscape. In this paper we prove error estimates for Euler discretization of high-index saddle dynamics with respect to the time step size, which remains untreated in the literature. We overcome the main difficulties that lie in the strong nonlinearity of the saddle dynamics and the orthonormalization procedure in the numerical scheme that is uncommon in standard discretization of differential equations. The derived methods are further extended to study the generalized high-index saddle dynamics for non-gradient systems and provide theoretical support for the accuracy of numerical implementations.
Cite
@article{arxiv.2111.05156,
title = {Error estimates for Euler discretization of high-index saddle dynamics},
author = {Lei Zhang and Pingwen Zhang and Xiangcheng Zheng},
journal= {arXiv preprint arXiv:2111.05156},
year = {2022}
}