A Numerical Solution of Fredholm Integral Equations of the Second Kind Based on Tight Framelets Generated by the Oblique Extension Principle
In this paper, we present a new computational method for solving linear Fredholm integral equations of the second kind, which is based on the use of <i>B</i>-spline quasi-affine tight framelet systems generated by the unitary and oblique extension principles. We convert the integral equa...
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| Format: | Article |
| Language: | English |
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MDPI AG
2019-07-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/11/7/854 |
| _version_ | 1811278859313610752 |
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| author | Mutaz Mohammad |
| author_facet | Mutaz Mohammad |
| author_sort | Mutaz Mohammad |
| collection | DOAJ |
| description | In this paper, we present a new computational method for solving linear Fredholm integral equations of the second kind, which is based on the use of <i>B</i>-spline quasi-affine tight framelet systems generated by the unitary and oblique extension principles. We convert the integral equation to a system of linear equations. We provide an example of the construction of quasi-affine tight framelet systems. We also give some numerical evidence to illustrate our method. The numerical results confirm that the method is efficient, very effective and accurate. |
| first_indexed | 2024-04-13T00:44:10Z |
| format | Article |
| id | doaj.art-448d19f750d24a1ca7e114cacefecee6 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-04-13T00:44:10Z |
| publishDate | 2019-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-448d19f750d24a1ca7e114cacefecee62022-12-22T03:10:04ZengMDPI AGSymmetry2073-89942019-07-0111785410.3390/sym11070854sym11070854A Numerical Solution of Fredholm Integral Equations of the Second Kind Based on Tight Framelets Generated by the Oblique Extension PrincipleMutaz Mohammad0Department of Mathematics and Statistics, College of Natural and Health Sciences, Zayed University, Abu Dhabi 144543, UAEIn this paper, we present a new computational method for solving linear Fredholm integral equations of the second kind, which is based on the use of <i>B</i>-spline quasi-affine tight framelet systems generated by the unitary and oblique extension principles. We convert the integral equation to a system of linear equations. We provide an example of the construction of quasi-affine tight framelet systems. We also give some numerical evidence to illustrate our method. The numerical results confirm that the method is efficient, very effective and accurate.https://www.mdpi.com/2073-8994/11/7/854Fredholm integral equationsmultiresolution analysisunitary extension principleoblique extension principle<i>B</i>-splineswaveletstight framelets |
| spellingShingle | Mutaz Mohammad A Numerical Solution of Fredholm Integral Equations of the Second Kind Based on Tight Framelets Generated by the Oblique Extension Principle Symmetry Fredholm integral equations multiresolution analysis unitary extension principle oblique extension principle <i>B</i>-splines wavelets tight framelets |
| title | A Numerical Solution of Fredholm Integral Equations of the Second Kind Based on Tight Framelets Generated by the Oblique Extension Principle |
| title_full | A Numerical Solution of Fredholm Integral Equations of the Second Kind Based on Tight Framelets Generated by the Oblique Extension Principle |
| title_fullStr | A Numerical Solution of Fredholm Integral Equations of the Second Kind Based on Tight Framelets Generated by the Oblique Extension Principle |
| title_full_unstemmed | A Numerical Solution of Fredholm Integral Equations of the Second Kind Based on Tight Framelets Generated by the Oblique Extension Principle |
| title_short | A Numerical Solution of Fredholm Integral Equations of the Second Kind Based on Tight Framelets Generated by the Oblique Extension Principle |
| title_sort | numerical solution of fredholm integral equations of the second kind based on tight framelets generated by the oblique extension principle |
| topic | Fredholm integral equations multiresolution analysis unitary extension principle oblique extension principle <i>B</i>-splines wavelets tight framelets |
| url | https://www.mdpi.com/2073-8994/11/7/854 |
| work_keys_str_mv | AT mutazmohammad anumericalsolutionoffredholmintegralequationsofthesecondkindbasedontightframeletsgeneratedbytheobliqueextensionprinciple AT mutazmohammad numericalsolutionoffredholmintegralequationsofthesecondkindbasedontightframeletsgeneratedbytheobliqueextensionprinciple |