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Mixed Spectral Method for Heat Transfer Using Generalised Hermite Functions and Legendre Polynomials

Published online by Cambridge University Press:  19 October 2016

Tian-Jun Wang*
Henan University of Science and Technology, Luoyang, 471003, China
Chao Zhang
Jiangsu Normal University, Xuzhou, 221116, China Jiangsu Key Laboratory of Education Big Data Science and Engineering, Xuzhou, 221116, China
Qiong Zhang
Henan University of Science and Technology, Luoyang, 471003, China
*Corresponding author. Email (T.-J. Wang)
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We propose amixed spectral method 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.

Research Article
Copyright © Global-Science Press 2016 

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