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: | , |
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| Format: | Article |
| Language: | English English English |
| Published: |
Elsevier
2018
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| Subjects: | |
| Online Access: | 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 http://irep.iium.edu.my/66316/ https://www.sciencedirect.com/science/article/pii/S2211379718314682 |
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| Summary: | 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. |
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