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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*
Affiliation:
Henan University of Science and Technology, Luoyang, 471003, China
Chao Zhang
Affiliation:
Jiangsu Normal University, Xuzhou, 221116, China Jiangsu Key Laboratory of Education Big Data Science and Engineering, Xuzhou, 221116, China
Qiong Zhang
Affiliation:
Henan University of Science and Technology, Luoyang, 471003, China
*
*Corresponding author. Email address:wangtianjun64@163.com (T.-J. Wang)
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Abstract

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.

Type
Research Article
Copyright
Copyright © Global-Science Press 2016 

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