3 papers
math.NA2024
An Adaptive Orthogonal Basis Method for Computing Multiple Solutions of Differential Equations with polynomial nonlinearities
Lin Li, Yangyi Ye, Huiyuan Li
This paper presents an innovative approach, the Adaptive Orthogonal Basis Method, tailored for computing multiple solutions to differential equations characterized by polynomial no…
math.NA2023
Müntz ball polynomials and Müntz spectral-Galerkin methods for singular eigenvalue problems
Xiu Yang, Li-Lian Wang, Huiyuan Li +1
In this paper, we introduce a new family of orthogonal systems, termed as the Müntz ball polynomials (MBPs), which are orthogonal with respect to the weight function: $\|x\|^{2θ+2μ…
math.NA2023
An Efficient Spectral Trust-Region Deflation Method for Multiple Solutions
Lin Li, Lilian Wang, Huiyuan Li
It is quite common that a nonlinear partial differential equation (PDE) admits multiple distinct solutions and each solution may carry a unique physical meaning. One typical approa…