Generalized Haar wavelet operational matrix method for solving hyperbolic heat conduction in thin surface layers

It is remarkably known that one of the difficulties encountered in a numerical method for hyperbolic heat conduction equation is the numerical oscillation within the vicinity of jump discontinuities at the wave front. In this paper, a new method is proposed for solving non-Fourier heat conduction...

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Main Authors:	Mt Aznam, Suazlan, Chowdhury, Md. Sazzad Hossien
Format:	Article
Language:	English English English
Published:	Elsevier 2018
Subjects:	QA Mathematics QA297 Numerical Analysis TP155 Chemical engineering
Online Access:	http://irep.iium.edu.my/66316/ http://irep.iium.edu.my/66316/ http://irep.iium.edu.my/66316/1/66316_Generalized%20Haar%20wavelet%20operational%20matrix.pdf http://irep.iium.edu.my/66316/2/66316_Generalized%20Haar%20wavelet%20operational%20matrix_SCOPUS.pdf http://irep.iium.edu.my/66316/13/66316%20Generalized%20Haar%20wavelet%20operational%20WOS.pdf

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spelling	iium-663162019-01-27T07:01:34Z http://irep.iium.edu.my/66316/ Generalized Haar wavelet operational matrix method for solving hyperbolic heat conduction in thin surface layers Mt Aznam, Suazlan Chowdhury, Md. Sazzad Hossien QA Mathematics QA297 Numerical Analysis TP155 Chemical engineering It is remarkably known that one of the difficulties encountered in a numerical method for hyperbolic heat conduction equation is the numerical oscillation within the vicinity of jump discontinuities at the wave front. In this paper, a new method is proposed for solving non-Fourier heat conduction problem. It is a combination of finite difference and pseudospectral methods in which the time discretization is performed prior to spatial discretization. In this sense, a partial differential equation is reduced to an ordinary differential equation and solved implicitly with Haar wavelet basis. For the pseudospectral method, Haar wavelet expansion has been using considering its advantage of the absence of the Gibbs phenomenon at the jump continuities. We also derived generalized Haar operational matrix that extend usual domain (0, 1] to (0, X]. The proposed method has been applied to one physical problem, namely thin surface layers. It is found that the proposed numerical results could suppress and eliminate the numerical oscillation in the vicinity jump and in good agreement with the analytic solution. In addition, our method is stable, convergent and easily coded. Numerical results demonstrate good performance of the method in term of accuracy and competitiveness compare to other numerical methods. Elsevier 2018-12 Article PeerReviewed application/pdf en http://irep.iium.edu.my/66316/1/66316_Generalized%20Haar%20wavelet%20operational%20matrix.pdf application/pdf en http://irep.iium.edu.my/66316/2/66316_Generalized%20Haar%20wavelet%20operational%20matrix_SCOPUS.pdf application/pdf en http://irep.iium.edu.my/66316/13/66316%20Generalized%20Haar%20wavelet%20operational%20WOS.pdf Mt Aznam, Suazlan and Chowdhury, Md. Sazzad Hossien (2018) Generalized Haar wavelet operational matrix method for solving hyperbolic heat conduction in thin surface layers. Results in Physics, 11. pp. 243-252. ISSN 2211-3797 https://www.sciencedirect.com/science/article/pii/S2211379718314682
repository_type	Digital Repository
institution_category	Local University
institution	International Islamic University Malaysia
building	IIUM Repository
collection	Online Access
language	English English English
topic	QA Mathematics QA297 Numerical Analysis TP155 Chemical engineering
spellingShingle	QA Mathematics QA297 Numerical Analysis TP155 Chemical engineering Mt Aznam, Suazlan Chowdhury, Md. Sazzad Hossien Generalized Haar wavelet operational matrix method for solving hyperbolic heat conduction in thin surface layers
description	It is remarkably known that one of the difficulties encountered in a numerical method for hyperbolic heat conduction equation is the numerical oscillation within the vicinity of jump discontinuities at the wave front. In this paper, a new method is proposed for solving non-Fourier heat conduction problem. It is a combination of finite difference and pseudospectral methods in which the time discretization is performed prior to spatial discretization. In this sense, a partial differential equation is reduced to an ordinary differential equation and solved implicitly with Haar wavelet basis. For the pseudospectral method, Haar wavelet expansion has been using considering its advantage of the absence of the Gibbs phenomenon at the jump continuities. We also derived generalized Haar operational matrix that extend usual domain (0, 1] to (0, X]. The proposed method has been applied to one physical problem, namely thin surface layers. It is found that the proposed numerical results could suppress and eliminate the numerical oscillation in the vicinity jump and in good agreement with the analytic solution. In addition, our method is stable, convergent and easily coded. Numerical results demonstrate good performance of the method in term of accuracy and competitiveness compare to other numerical methods.
format	Article
author	Mt Aznam, Suazlan Chowdhury, Md. Sazzad Hossien
author_facet	Mt Aznam, Suazlan Chowdhury, Md. Sazzad Hossien
author_sort	Mt Aznam, Suazlan
title	Generalized Haar wavelet operational matrix method for solving hyperbolic heat conduction in thin surface layers
title_short	Generalized Haar wavelet operational matrix method for solving hyperbolic heat conduction in thin surface layers
title_full	Generalized Haar wavelet operational matrix method for solving hyperbolic heat conduction in thin surface layers
title_fullStr	Generalized Haar wavelet operational matrix method for solving hyperbolic heat conduction in thin surface layers
title_full_unstemmed	Generalized Haar wavelet operational matrix method for solving hyperbolic heat conduction in thin surface layers
title_sort	generalized haar wavelet operational matrix method for solving hyperbolic heat conduction in thin surface layers
publisher	Elsevier
publishDate	2018
url	http://irep.iium.edu.my/66316/ http://irep.iium.edu.my/66316/ http://irep.iium.edu.my/66316/1/66316_Generalized%20Haar%20wavelet%20operational%20matrix.pdf http://irep.iium.edu.my/66316/2/66316_Generalized%20Haar%20wavelet%20operational%20matrix_SCOPUS.pdf http://irep.iium.edu.my/66316/13/66316%20Generalized%20Haar%20wavelet%20operational%20WOS.pdf
first_indexed	2023-09-18T21:34:08Z
last_indexed	2023-09-18T21:34:08Z
_version_	1777412707053469696

Generalized Haar wavelet operational matrix method for solving hyperbolic heat conduction in thin surface layers

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