3 papers
math.NA2026
Scaling Optimized Spectral Approximations on Unbounded Domains: The Generalized Hermite and Laguerre Methods
Hao Hu, Haijun Yu
We propose a novel error analysis framework for scaled generalized Laguerre and generalized Hermite approximations.This framework can be regarded as an analogue of the Nyquist-Shan…
math.NA2026
Moving sample method for solving time-dependent partial differential equations
Beining Xu, Haijun Yu, Jiayu Zhai +2
Solving time-dependent partial differential equations (PDEs) that exhibit sharp gradients or local singularities is computationally demanding, as traditional physics-informed neura…
math.NA2025
An Improved Adaptive Orthogonal Basis Deflation Method for Multiple Solutions with Applications to Nonlinear Elliptic Equations in Varying Domains
Yangyi Ye, Lin Li, Pengcheng Xie +1
Multiple solutions are common in various non-convex problems arising from industrial and scientific computing. Nonetheless, understanding the nontrivial solutions' qualitative prop…