Volume 6, Issue 4
Mixed Spectral Method for Heat Transfer Using Generalised Hermite Functions and Legendre Polynomials

Tian-Jun Wang, Chao Zhang & Qiong Zhang

East Asian J. Appl. Math., 6 (2016), pp. 448-465.

Published online: 2018-02

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  • Abstract

We propose amixed spectralmethod for heat transfer in unbounded domains, using generalised Hermite functions and Legendre polynomials. Some basic results on the mixed generalised Hermite-Legendre orthogonal approximation are established, which plays important roles in spectral methods for various problems defined on unbounded domains. As an example, the mixed generalised Hermite-Legendre spectral scheme is constructed for anisotropic heat transfer. Its convergence is proven, and some numerical results demonstrate the spectral accuracy of this approach.

  • Keywords

The scaled generalised Hermite functions, mixed spectral method, anisotropic heat transfer, unbounded domains.

  • AMS Subject Headings

33C45, 76M22, 65N12, 35K15, 35K20

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{EAJAM-6-448, author = {}, title = {Mixed Spectral Method for Heat Transfer Using Generalised Hermite Functions and Legendre Polynomials}, journal = {East Asian Journal on Applied Mathematics}, year = {2018}, volume = {6}, number = {4}, pages = {448--465}, abstract = {

We propose amixed spectralmethod for heat transfer in unbounded domains, using generalised Hermite functions and Legendre polynomials. Some basic results on the mixed generalised Hermite-Legendre orthogonal approximation are established, which plays important roles in spectral methods for various problems defined on unbounded domains. As an example, the mixed generalised Hermite-Legendre spectral scheme is constructed for anisotropic heat transfer. Its convergence is proven, and some numerical results demonstrate the spectral accuracy of this approach.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.231015.240816a}, url = {http://global-sci.org/intro/article_detail/eajam/10812.html} }
TY - JOUR T1 - Mixed Spectral Method for Heat Transfer Using Generalised Hermite Functions and Legendre Polynomials JO - East Asian Journal on Applied Mathematics VL - 4 SP - 448 EP - 465 PY - 2018 DA - 2018/02 SN - 6 DO - http://doi.org/10.4208/eajam.231015.240816a UR - https://global-sci.org/intro/article_detail/eajam/10812.html KW - The scaled generalised Hermite functions, mixed spectral method, anisotropic heat transfer, unbounded domains. AB -

We propose amixed spectralmethod for heat transfer in unbounded domains, using generalised Hermite functions and Legendre polynomials. Some basic results on the mixed generalised Hermite-Legendre orthogonal approximation are established, which plays important roles in spectral methods for various problems defined on unbounded domains. As an example, the mixed generalised Hermite-Legendre spectral scheme is constructed for anisotropic heat transfer. Its convergence is proven, and some numerical results demonstrate the spectral accuracy of this approach.

Tian-Jun Wang, Chao Zhang & Qiong Zhang. (2020). Mixed Spectral Method for Heat Transfer Using Generalised Hermite Functions and Legendre Polynomials. East Asian Journal on Applied Mathematics. 6 (4). 448-465. doi:10.4208/eajam.231015.240816a
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