3 papers
math.NA2026
Numerical analysis of spatiotemporal high-index saddle dynamics for finding multiple solutions of semilinear elliptic problems
Lei Zhang, Xiangcheng Zheng, Shangqin Zhu
This paper presents a rigorous numerical framework for computing multiple solutions of semilinear elliptic problems by spatiotemporal high-index saddle dynamics (HiSD), which exten…
math.NA2025
Numerical analysis for saddle dynamics of some semilinear elliptic problems
Lei Zhang, Xiangcheng Zheng, Shangqin Zhu
This work presents a numerical analysis of computing transition states of semilinear elliptic partial differential equations (PDEs) via the index-1 saddle dynamics, or equivalently…
math.CA2024
Weighted Sonine conditions and application
Xiangcheng Zheng, Shangqin Zhu, Yiqun Li
The Sonine kernel described by the classical Sonine condition of convolution form is an important class of kernels used in integral equations and nonlocal differential equations. T…