1 citations · 1 across the 3 of their papers we have counts for
3 papers
math.NA2025
A new banded Petrov--Galerkin spectral method
Ouyuan Qin, Lu Cheng, Kuan Xu
We propose a Petrov--Galerkin spectral method for ODEs with variable coefficients. When the variable coefficients are smooth, the new method yields a strictly banded linear system,…
math.NA2024★ 1 cited
Understanding the ultraspherical spectral method
Lu Cheng, Kuan Xu
The ultraspherical spectral method features high accuracy and fast solution. In this article, we determine the sources of error arising from the ultraspherical spectral method and…
math.NA2023
Solving time-dependent PDEs with the ultraspherical spectral method
Lu Cheng, Kuan Xu
We apply the ultraspherical spectral method to solving time-dependent PDEs by proposing two approaches to discretization based on the method of lines and show that these approaches…