Numerical method for inverse laplace transform with Haar wavelet operational matrix
Wavelets have been applied successfully in signal and image processing. Many attempts have been made in mathematics to use orthogonal wavelet function as numerical computational tool. In this work, an orthogonal wavelet function namely Haar wavelet function is considered. We present a numerical me...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
UTM Press
2012
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| Subjects: | |
| Online Access: | http://irep.iium.edu.my/65471/ http://irep.iium.edu.my/65471/ http://irep.iium.edu.my/65471/ http://irep.iium.edu.my/65471/1/149-1530-1-PB.pdf |
| Summary: | Wavelets have been applied successfully in signal and image processing. Many attempts have been made in mathematics to use orthogonal wavelet
function as numerical computational tool. In this work, an orthogonal wavelet function namely Haar wavelet function is considered. We present a
numerical method for inversion of Laplace transform using the method of Haar wavelet operational matrix for integration. We proved the method for the
cases of the irrational transfer function using the extension of Riemenn-Liouville fractional integral. The proposed method extends the work of J.L.Wu et
al. (2001) to cover the whole of time domain. Moreover, this work gives an alternative way to find the solution for inversion of Laplace transform in a
faster way. The use of numerical Haar operational matrix method is much simpler than the conventional contour integration method and it can be easily
coded. Additionally, few benefits come from its great features such as faster computation and attractiveness. Numerical results demonstrate good
performance of the method in term of accuracy and competitiveness compare to analytical solution. Examples on solving differential equation by Laplace
transform method are also given. |
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