Approximate Methods for Calculating Singular and Hypersingular Integrals with Rapidly Oscillating Kernels
The article is devoted to the issue of construction of an optimal with respect to order passive algorithms for evaluating Cauchy and Hilbert singular and hypersingular integrals with oscillating kernels. We propose a method for estimating lower bound errors of quadrature formulas for singular and hy...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-03-01
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| Series: | Axioms |
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| Online Access: | https://www.mdpi.com/2075-1680/11/4/150 |
| _version_ | 1797436909813760000 |
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| author | Ilya Boykov Vladimir Roudnev Alla Boykova |
| author_facet | Ilya Boykov Vladimir Roudnev Alla Boykova |
| author_sort | Ilya Boykov |
| collection | DOAJ |
| description | The article is devoted to the issue of construction of an optimal with respect to order passive algorithms for evaluating Cauchy and Hilbert singular and hypersingular integrals with oscillating kernels. We propose a method for estimating lower bound errors of quadrature formulas for singular and hypersingular integral evaluation. Quadrature formulas were constructed for implementation of the obtained estimates. We constructed quadrature formulas and estimated the errors for hypersingular integrals with oscillating kernels. This method is based on using similar results obtained for singular integrals. |
| first_indexed | 2024-03-09T11:10:21Z |
| format | Article |
| id | doaj.art-ba2931f82ac341fbb391415cab4d0417 |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-03-09T11:10:21Z |
| publishDate | 2022-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-ba2931f82ac341fbb391415cab4d04172023-12-01T00:48:11ZengMDPI AGAxioms2075-16802022-03-0111415010.3390/axioms11040150Approximate Methods for Calculating Singular and Hypersingular Integrals with Rapidly Oscillating KernelsIlya Boykov0Vladimir Roudnev1Alla Boykova2Department of Higher and Applied Mathematics, Penza State University, Penza 440026, RussiaDepartment of Computational Physics, Saint Petersburg State University, 7/9 Universitetskaya Emb., Saint Petersburg 199034, RussiaDepartment of Higher and Applied Mathematics, Penza State University, Penza 440026, RussiaThe article is devoted to the issue of construction of an optimal with respect to order passive algorithms for evaluating Cauchy and Hilbert singular and hypersingular integrals with oscillating kernels. We propose a method for estimating lower bound errors of quadrature formulas for singular and hypersingular integral evaluation. Quadrature formulas were constructed for implementation of the obtained estimates. We constructed quadrature formulas and estimated the errors for hypersingular integrals with oscillating kernels. This method is based on using similar results obtained for singular integrals.https://www.mdpi.com/2075-1680/11/4/150singular integralshypersingular integralsoptimal quadrature formulasoscillating kernelserror estimation |
| spellingShingle | Ilya Boykov Vladimir Roudnev Alla Boykova Approximate Methods for Calculating Singular and Hypersingular Integrals with Rapidly Oscillating Kernels Axioms singular integrals hypersingular integrals optimal quadrature formulas oscillating kernels error estimation |
| title | Approximate Methods for Calculating Singular and Hypersingular Integrals with Rapidly Oscillating Kernels |
| title_full | Approximate Methods for Calculating Singular and Hypersingular Integrals with Rapidly Oscillating Kernels |
| title_fullStr | Approximate Methods for Calculating Singular and Hypersingular Integrals with Rapidly Oscillating Kernels |
| title_full_unstemmed | Approximate Methods for Calculating Singular and Hypersingular Integrals with Rapidly Oscillating Kernels |
| title_short | Approximate Methods for Calculating Singular and Hypersingular Integrals with Rapidly Oscillating Kernels |
| title_sort | approximate methods for calculating singular and hypersingular integrals with rapidly oscillating kernels |
| topic | singular integrals hypersingular integrals optimal quadrature formulas oscillating kernels error estimation |
| url | https://www.mdpi.com/2075-1680/11/4/150 |
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