Construction and Analysis for Adams Explicit Discretization of High-Index Saddle Dynamics (CSIAM Transactions on Applied Mathematics, 2025)
Saddle points largely exist in complex systems and play important roles invarious scientific problems. High-index saddle dynamics (HiSD) is an efficient methodfor computing any-index saddle points and constructing solution landscape. In thispaper, 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-stepAdams explicit scheme has second-order accuracy. The theoretical results are furtherverified by two numerical experiments.
Keywords: Saddle point; saddle dynamics; solution landscape; Adams scheme; error estimate.