New algorithms for numerical assessment of nonlinear integro-differential equations of second-order using Haar wavelets
This paper deals with the extended design for Fredholm and Volterra integral equations and design for Fredholm and Volterra integro-differential equations of first-order to second-order nonlinear Fredholm and second-order nonlinear Volterra integro-differential equations having square integrable ker...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English English |
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Walailak University,Thailand
2015
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| Subjects: | |
| Online Access: | http://irep.iium.edu.my/44552/ http://irep.iium.edu.my/44552/1/1065-16740-2-PB.pdf http://irep.iium.edu.my/44552/4/44552_new_algorithms_Scopus.pdf |
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| author | Aziz, Imran Ul-Islam, Siraj Fayyaz, Muhammad Azram, Mohammad |
| author_facet | Aziz, Imran Ul-Islam, Siraj Fayyaz, Muhammad Azram, Mohammad |
| author_sort | Aziz, Imran |
| building | IIUM Repository |
| collection | Online Access |
| description | This paper deals with the extended design for Fredholm and Volterra integral equations and design for Fredholm and Volterra integro-differential equations of first-order to second-order nonlinear Fredholm and second-order nonlinear Volterra integro-differential equations having square integrable kernels. This approach utilizes the inherent dynamics of the Haar wavelet. The Haar wavelet is used to provide a single platform for the proposed method. The method is tested on problems from literature, and numerical results are compared with existing methods. The numerical results indicate that the accuracy of the method is reasonably high, even on a coarse grid. |
| first_indexed | 2025-11-14T16:08:25Z |
| format | Article |
| id | iium-44552 |
| institution | International Islamic University Malaysia |
| institution_category | Local University |
| language | English English |
| last_indexed | 2025-11-14T16:08:25Z |
| publishDate | 2015 |
| publisher | Walailak University,Thailand |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | iium-445522017-11-21T09:14:33Z http://irep.iium.edu.my/44552/ New algorithms for numerical assessment of nonlinear integro-differential equations of second-order using Haar wavelets Aziz, Imran Ul-Islam, Siraj Fayyaz, Muhammad Azram, Mohammad QA Mathematics This paper deals with the extended design for Fredholm and Volterra integral equations and design for Fredholm and Volterra integro-differential equations of first-order to second-order nonlinear Fredholm and second-order nonlinear Volterra integro-differential equations having square integrable kernels. This approach utilizes the inherent dynamics of the Haar wavelet. The Haar wavelet is used to provide a single platform for the proposed method. The method is tested on problems from literature, and numerical results are compared with existing methods. The numerical results indicate that the accuracy of the method is reasonably high, even on a coarse grid. Walailak University,Thailand 2015 Article PeerReviewed application/pdf en http://irep.iium.edu.my/44552/1/1065-16740-2-PB.pdf application/pdf en http://irep.iium.edu.my/44552/4/44552_new_algorithms_Scopus.pdf Aziz, Imran and Ul-Islam, Siraj and Fayyaz, Muhammad and Azram, Mohammad (2015) New algorithms for numerical assessment of nonlinear integro-differential equations of second-order using Haar wavelets. Walailak Journal of Science and Technology (WJST), 12 (11). pp. 995-1007. ISSN 2228-835X (O), 1686-3933 (P) http://wjst.wu.ac.th/index.php/wjst/article/view/1065 |
| spellingShingle | QA Mathematics Aziz, Imran Ul-Islam, Siraj Fayyaz, Muhammad Azram, Mohammad New algorithms for numerical assessment of nonlinear integro-differential equations of second-order using Haar wavelets |
| title | New algorithms for numerical assessment of nonlinear integro-differential equations of second-order using Haar wavelets |
| title_full | New algorithms for numerical assessment of nonlinear integro-differential equations of second-order using Haar wavelets |
| title_fullStr | New algorithms for numerical assessment of nonlinear integro-differential equations of second-order using Haar wavelets |
| title_full_unstemmed | New algorithms for numerical assessment of nonlinear integro-differential equations of second-order using Haar wavelets |
| title_short | New algorithms for numerical assessment of nonlinear integro-differential equations of second-order using Haar wavelets |
| title_sort | new algorithms for numerical assessment of nonlinear integro-differential equations of second-order using haar wavelets |
| topic | QA Mathematics |
| url | http://irep.iium.edu.my/44552/ http://irep.iium.edu.my/44552/ http://irep.iium.edu.my/44552/1/1065-16740-2-PB.pdf http://irep.iium.edu.my/44552/4/44552_new_algorithms_Scopus.pdf |