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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…