A collocation method via the quasi-affine biorthogonal systems for solving weakly singular type of Volterra-Fredholm integral equations
Tight framelet system is a recently developed tool in applied mathematics. Framelets, due to their nature, are widely used in the area of image manipulation, data compression, numerical analysis, engineering mathematical problems such as inverse problems, visco-elasticity or creep problems, and many...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Elsevier
2020-08-01
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| Series: | Alexandria Engineering Journal |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S1110016820300478 |
| _version_ | 1818436627680198656 |
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| author | Mutaz Mohammad Carlo Cattani |
| author_facet | Mutaz Mohammad Carlo Cattani |
| author_sort | Mutaz Mohammad |
| collection | DOAJ |
| description | Tight framelet system is a recently developed tool in applied mathematics. Framelets, due to their nature, are widely used in the area of image manipulation, data compression, numerical analysis, engineering mathematical problems such as inverse problems, visco-elasticity or creep problems, and many more. In this manuscript we provide a numerical solution of important weakly singular type of Volterra - Fredholm integral equations WSVFIEs using the collocation type quasi-affine biorthogonal method. We present a new computational method based on special B-spline tight framelets and use it to introduce our numerical scheme. The method provides a robust solution for the given WSVFIE by using the resulting matrices based on these biorthogonal wavelet. We demonstrate the validity and accuracy of the proposed method by some numerical examples. |
| first_indexed | 2024-12-14T17:11:47Z |
| format | Article |
| id | doaj.art-52277a7d87d541b5bc2d201805f7b7e2 |
| institution | Directory Open Access Journal |
| issn | 1110-0168 |
| language | English |
| last_indexed | 2024-12-14T17:11:47Z |
| publishDate | 2020-08-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Alexandria Engineering Journal |
| spelling | doaj.art-52277a7d87d541b5bc2d201805f7b7e22022-12-21T22:53:31ZengElsevierAlexandria Engineering Journal1110-01682020-08-0159421812191A collocation method via the quasi-affine biorthogonal systems for solving weakly singular type of Volterra-Fredholm integral equationsMutaz Mohammad0Carlo Cattani1Zayed University, Abu Dhabi, United Arab Emirates; Corresponding author.Engineering School, DEIM, Tuscia University, Viterbo, ItalyTight framelet system is a recently developed tool in applied mathematics. Framelets, due to their nature, are widely used in the area of image manipulation, data compression, numerical analysis, engineering mathematical problems such as inverse problems, visco-elasticity or creep problems, and many more. In this manuscript we provide a numerical solution of important weakly singular type of Volterra - Fredholm integral equations WSVFIEs using the collocation type quasi-affine biorthogonal method. We present a new computational method based on special B-spline tight framelets and use it to introduce our numerical scheme. The method provides a robust solution for the given WSVFIE by using the resulting matrices based on these biorthogonal wavelet. We demonstrate the validity and accuracy of the proposed method by some numerical examples.http://www.sciencedirect.com/science/article/pii/S1110016820300478Unitary extension principleTight frameletsQuasi-affine systemB-splinesWeakly singular Volterra- Fredholm integral equations |
| spellingShingle | Mutaz Mohammad Carlo Cattani A collocation method via the quasi-affine biorthogonal systems for solving weakly singular type of Volterra-Fredholm integral equations Alexandria Engineering Journal Unitary extension principle Tight framelets Quasi-affine system B-splines Weakly singular Volterra- Fredholm integral equations |
| title | A collocation method via the quasi-affine biorthogonal systems for solving weakly singular type of Volterra-Fredholm integral equations |
| title_full | A collocation method via the quasi-affine biorthogonal systems for solving weakly singular type of Volterra-Fredholm integral equations |
| title_fullStr | A collocation method via the quasi-affine biorthogonal systems for solving weakly singular type of Volterra-Fredholm integral equations |
| title_full_unstemmed | A collocation method via the quasi-affine biorthogonal systems for solving weakly singular type of Volterra-Fredholm integral equations |
| title_short | A collocation method via the quasi-affine biorthogonal systems for solving weakly singular type of Volterra-Fredholm integral equations |
| title_sort | collocation method via the quasi affine biorthogonal systems for solving weakly singular type of volterra fredholm integral equations |
| topic | Unitary extension principle Tight framelets Quasi-affine system B-splines Weakly singular Volterra- Fredholm integral equations |
| url | http://www.sciencedirect.com/science/article/pii/S1110016820300478 |
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