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...
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| Format: | Article |
| Language: | English |
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UTM Press
2012
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| Online Access: | http://irep.iium.edu.my/65471/ http://irep.iium.edu.my/65471/1/149-1530-1-PB.pdf |
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| author | Mt Aznam, Suazlan Hussin, Amran |
| author_facet | Mt Aznam, Suazlan Hussin, Amran |
| author_sort | Mt Aznam, Suazlan |
| building | IIUM Repository |
| collection | Online Access |
| description | 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. |
| first_indexed | 2025-11-14T17:08:21Z |
| format | Article |
| id | iium-65471 |
| institution | International Islamic University Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T17:08:21Z |
| publishDate | 2012 |
| publisher | UTM Press |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | iium-654712018-09-14T07:17:52Z http://irep.iium.edu.my/65471/ Numerical method for inverse laplace transform with Haar wavelet operational matrix Mt Aznam, Suazlan Hussin, Amran QA297 Numerical Analysis 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. UTM Press 2012-10 Article PeerReviewed application/pdf en http://irep.iium.edu.my/65471/1/149-1530-1-PB.pdf Mt Aznam, Suazlan and Hussin, Amran (2012) Numerical method for inverse laplace transform with Haar wavelet operational matrix. Malaysian Journal of Fundamental and Applied Sciences, 8 (4 (October-December)). pp. 204-210. ISSN 2289-5981 E-ISSN 2289-599X https://mjfas.utm.my/index.php/mjfas/article/view/149/429 10.11113/mjfas.v8n4.149 |
| spellingShingle | QA297 Numerical Analysis Mt Aznam, Suazlan Hussin, Amran Numerical method for inverse laplace transform with Haar wavelet operational matrix |
| title | Numerical method for inverse laplace transform with Haar wavelet operational matrix |
| title_full | Numerical method for inverse laplace transform with Haar wavelet operational matrix |
| title_fullStr | Numerical method for inverse laplace transform with Haar wavelet operational matrix |
| title_full_unstemmed | Numerical method for inverse laplace transform with Haar wavelet operational matrix |
| title_short | Numerical method for inverse laplace transform with Haar wavelet operational matrix |
| title_sort | numerical method for inverse laplace transform with haar wavelet operational matrix |
| topic | QA297 Numerical Analysis |
| url | 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 |