Superconvergence points of Hermite spectral interpolation
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866912493630128128 |
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| author | Wang, Haiyong Zhang, Zhimin |
| author_facet | Wang, Haiyong Zhang, Zhimin |
| contents | Hermite spectral method plays an important role in the numerical simulation of various partial differential equations (PDEs) on unbounded domains. In this work, we study the superconvergence properties of Hermite spectral interpolation, i.e., interpolation at the zeros of Hermite polynomials in the space spanned by Hermite functions. We identify the points at which the convergence rates of the first- and second-order derivatives of the interpolant converge faster. We further extend the analysis to the Hermite spectral collocation method in solving differential equations and identify the superconvergence points both for function and derivative values. Numerical examples are provided to confirm the analysis of superconvergence points. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_15350 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Superconvergence points of Hermite spectral interpolation Wang, Haiyong Zhang, Zhimin Numerical Analysis 41A05, 41A25, 65N35, 65D05 Hermite spectral method plays an important role in the numerical simulation of various partial differential equations (PDEs) on unbounded domains. In this work, we study the superconvergence properties of Hermite spectral interpolation, i.e., interpolation at the zeros of Hermite polynomials in the space spanned by Hermite functions. We identify the points at which the convergence rates of the first- and second-order derivatives of the interpolant converge faster. We further extend the analysis to the Hermite spectral collocation method in solving differential equations and identify the superconvergence points both for function and derivative values. Numerical examples are provided to confirm the analysis of superconvergence points. |
| title | Superconvergence points of Hermite spectral interpolation |
| topic | Numerical Analysis 41A05, 41A25, 65N35, 65D05 |
| url | https://arxiv.org/abs/2507.15350 |