Hermite spectral approximation for functions with endpoint singularities using exponential transforms
Year: 2026
Type: preprint
Abstract: In this paper we introduce Hermite spectral approximation for functions with endpoint singularities using exponential transforms, including single exponential (SE), double exponential (DE) and error function (EF) transforms, and present a comprehensive convergence analysis for these approximations without and with scaling. In the case without scaling, we show that these methods converge at some root-exponential rate. In the case with scaling, we derive optimal scaling factors for each of exponential transforms and show that the convergence rate of Hermite spectral approximation can be significantly improved. Numerical comparisons with sinc method are present and it is shown that Hermite method has comparable or superior accuracy performance when using the same number of terms. Extensions to quadrature and rootfinding algorithm are also discussed.
Source: arXiv (Cornell University)
Author: Wang, Haiyong
Institution: Huazhong University of Science and Technology
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7168360934
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