33 citations · 45 across the 7 of their papers we have counts for
7 papers
Accelerated Nehari manifold optimization methods for computing ground state solutions of coupled elliptic systems
Zhaoxing Chen, Wei Liu, Ziqing Xie +1
This paper presents a class of efficient algorithms for computing the ground state solutions of a semilinear elliptic system, which are unstable saddle points of the variational fu…
A Convergent Inexact Abedin-Kitagawa Iteration Method for Monge-Ampère Eigenvalue Problems
Liang Chen, Youyicun Lin, Junqi Yang +1
This paper proposes an inexact Aleksandrov-solution-based iteration method, formulated by adapting the convergent Rayleigh inverse iterative scheme introduced by Abedin and Kitagaw…
Nehari manifold optimization and its application for finding unstable solutions of semilinear elliptic PDEs
Zhaoxing Chen, Wei Liu, Ziqing Xie +1
A Nehari manifold optimization method (NMOM) is introduced for finding 1-saddles, i.e., saddle points with the Morse index equal to one, of a generic nonlinear functional in Hilber…
Nonmonotone local minimax methods for finding multiple saddle points
Wei Liu, Ziqing Xie, Wenfan Yi
In this paper, by designing a normalized nonmonotone search strategy with the Barzilai--Borwein-type step-size, a novel local minimax method (LMM), which is a globally convergent i…
Normalized Wolfe-Powell-type local minimax method for finding multiple unstable solutions of nonlinear elliptic PDEs
Wei Liu, Ziqing Xie, Wenfan Yi
The local minimax method (LMM) proposed in [Y. Li and J. Zhou, SIAM J. Sci. Comput., 23(3), 840--865 (2001)] and [Y. Li and J. Zhou, SIAM J. Sci. Comput., 24(3), 865--885 (2002)] i…
Uniform error bounds of an exponential wave integrator for the long-time dynamics of the nonlinear Klein-Gordon equation
Yue Feng, Wenfan Yi
We establish uniform error bounds of an exponential wave integrator Fourier pseudospectral (EWI-FP) method for the long-time dynamics of the nonlinear Klein-Gordon equation (NKGE)…
Long time error analysis of finite difference time domain methods for the nonlinear Klein-Gordon equation with weak nonlinearity
Weizhu Bao, Yue Feng, Wenfan Yi
We establish error bounds of the finite difference time domain (FDTD) methods for the long time dynamics of the nonlinear Klein-Gordon equation (NKGE) with a cubic nonlinearity, wh…