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

Part of: Partial differential equations, boundary value problems Parabolic equations and systems Basic methods in fluid mechanics

Published online by Cambridge University Press:  19 October 2016

Tian-Jun Wang ,
Chao Zhang  and
Qiong Zhang
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.

Keywords

The scaled generalised Hermite functionsmixed spectral methodanisotropic heat transferunbounded domains

MSC classification

Secondary: 33C45: Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) 76M22: Spectral methods 65N12: Stability and convergence of numerical methods 35K15: Initial value problems for second-order parabolic equations 35K20: Initial-boundary value problems for second-order parabolic equations
Type
Research Article
Information
East Asian Journal on Applied Mathematics , Volume 6 , Issue 4 , November 2016 , pp. 448 - 465
Copyright
Copyright © Global-Science Press 2016 

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