TY - JOUR
T1 - Construction and Analysis for Adams Explicit Discretization of High-Index Saddle Dynamics
AU - Miao , Shuai
AU - Liu , Ziqi
AU - Zhang , Lei
AU - Zhang , Pingwen
AU - Zheng , Xiangcheng
JO - CSIAM Transactions on Applied Mathematics
VL - 3
SP - 625
EP - 650
PY - 2025
DA - 2025/09
SN - 6
DO - http://doi.org/10.4208/csiam-am.SO-2024-0020
UR - https://global-sci.org/intro/article_detail/csiam-am/24377.html
KW - Saddle point, saddle dynamics, solution landscape, Adams scheme, error estimate.
AB - <p style="text-align: justify;">Saddle points largely exist in complex systems and play important roles in
various scientific problems. High-index saddle dynamics (HiSD) is an efficient method
for computing any-index saddle points and constructing solution landscape. In this
paper, we propose a two-step Adams explicit scheme for HiSD and analyze its error estimate versus time step. Through careful argumentation and overcoming the difficulties caused by nonlinear coupling and orthogonalisation, we prove that the two-step
Adams explicit scheme has second-order accuracy. The theoretical results are further
verified by two numerical experiments.</p>