3 papers
math.NA2026
High-Precision Phase-Shift Transferable Neural Networks for High-Frequency Function Approximation and PDE Solution
Xuyang Gao, Liang Chen, Minqiang Xu +1
Neural network based methods have emerged as a promising paradigm for scientific computing, yet they face critical bottlenecks in high frequency function approximation and partial…
math.NA2025
A Random Integration Algorithm for High-dimensional Function Spaces
Liang Chen, Minqiang Xu, Haizhang Zhang
We introduce a novel random integration algorithm that boasts both high convergence order and polynomial tractability for functions characterized by sparse frequencies or rapidly d…
math.NA2025
A class of positive-preserving,energy stable and high order numerical schemes for the Poission-Nernst-Planck system
Waixiang Cao, Yuzhe Qin, Minqiang Xu
In this paper, we introduce and analyze a class of numerical schemes that demonstrate remarkable superiority in terms of efficiency, the preservation of positivity, energy stabilit…