Construction and Analysis for Adams Explicit Discretization of High-Index Saddle Dynamics

Abstract

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.

Keywords

Saddle point / saddle dynamics / solution landscape / Adams scheme / error estimate