Biorthogonal-Wavelet-Based Method for Numerical Solution of Volterra Integral Equations
Framelets theory has been well studied in many applications in image processing, data recovery and computational analysis due to the key properties of framelets such as sparse representation and accuracy in coefficients recovery in the area of numerical and computational theory. This work is devoted...
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| Format: | Article |
| Language: | English |
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MDPI AG
2019-11-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/21/11/1098 |
| _version_ | 1798003583573032960 |
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| author | Mutaz Mohammad |
| author_facet | Mutaz Mohammad |
| author_sort | Mutaz Mohammad |
| collection | DOAJ |
| description | Framelets theory has been well studied in many applications in image processing, data recovery and computational analysis due to the key properties of framelets such as sparse representation and accuracy in coefficients recovery in the area of numerical and computational theory. This work is devoted to shedding some light on the benefits of using such framelets in the area of numerical computations of integral equations. We introduce a new numerical method for solving Volterra integral equations. It is based on pseudo-spline quasi-affine tight framelet systems generated via the oblique extension principles. The resulting system is converted into matrix equations via these generators. We present examples of the generated pseudo-splines quasi-affine tight framelet systems. Some numerical results to validate the proposed method are presented to illustrate the efficiency and accuracy of the method. |
| first_indexed | 2024-04-11T12:10:02Z |
| format | Article |
| id | doaj.art-d7ab995c575f4ab4a15dcaa8e03ed1c8 |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-04-11T12:10:02Z |
| publishDate | 2019-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-d7ab995c575f4ab4a15dcaa8e03ed1c82022-12-22T04:24:38ZengMDPI AGEntropy1099-43002019-11-012111109810.3390/e21111098e21111098Biorthogonal-Wavelet-Based Method for Numerical Solution of Volterra Integral EquationsMutaz Mohammad0Department of Mathematics and Statistics, College of Natural and Health Sciences, Zayed University, 144543 Abu Dhabi, UAEFramelets theory has been well studied in many applications in image processing, data recovery and computational analysis due to the key properties of framelets such as sparse representation and accuracy in coefficients recovery in the area of numerical and computational theory. This work is devoted to shedding some light on the benefits of using such framelets in the area of numerical computations of integral equations. We introduce a new numerical method for solving Volterra integral equations. It is based on pseudo-spline quasi-affine tight framelet systems generated via the oblique extension principles. The resulting system is converted into matrix equations via these generators. We present examples of the generated pseudo-splines quasi-affine tight framelet systems. Some numerical results to validate the proposed method are presented to illustrate the efficiency and accuracy of the method.https://www.mdpi.com/1099-4300/21/11/1098volterra integral equationsmultiresolution analysisoblique extension principlepseudo-splinesbiorthogonal waveletsquasi-affine systems |
| spellingShingle | Mutaz Mohammad Biorthogonal-Wavelet-Based Method for Numerical Solution of Volterra Integral Equations Entropy volterra integral equations multiresolution analysis oblique extension principle pseudo-splines biorthogonal wavelets quasi-affine systems |
| title | Biorthogonal-Wavelet-Based Method for Numerical Solution of Volterra Integral Equations |
| title_full | Biorthogonal-Wavelet-Based Method for Numerical Solution of Volterra Integral Equations |
| title_fullStr | Biorthogonal-Wavelet-Based Method for Numerical Solution of Volterra Integral Equations |
| title_full_unstemmed | Biorthogonal-Wavelet-Based Method for Numerical Solution of Volterra Integral Equations |
| title_short | Biorthogonal-Wavelet-Based Method for Numerical Solution of Volterra Integral Equations |
| title_sort | biorthogonal wavelet based method for numerical solution of volterra integral equations |
| topic | volterra integral equations multiresolution analysis oblique extension principle pseudo-splines biorthogonal wavelets quasi-affine systems |
| url | https://www.mdpi.com/1099-4300/21/11/1098 |
| work_keys_str_mv | AT mutazmohammad biorthogonalwaveletbasedmethodfornumericalsolutionofvolterraintegralequations |