Regularization of divergent integrals: A comparison of the classical and generalized-functions approaches
This article considers methods of weakly singular and hypersingular integral regularization based on the theory of distributions. For regularization of divergent integrals, the Gauss–Ostrogradskii theorem and the second Green’s theorem in the sense of the theory of distribution have been used. Equations that allow easy calculation of weakly singular, singular, and hypersingular integrals in one- and two-dimensional cases for any sufficiently smooth function have been obtained. These equations are compared with classical methods of regularization. The results of numerical calculation using classical approaches and those based of the theory of generalized functions, along with a comparison for different functions, are presented in tables and graphs of the values of divergent integrals versus the position of the colocation point.
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| Format: | info:eu-repo/semantics/article biblioteca |
| Language: | eng |
| Subjects: | info:eu-repo/classification/Autores/BEM, info:eu-repo/classification/Autores/BIE, info:eu-repo/classification/Autores/DIVERGENT, info:eu-repo/classification/Autores/GENERALIZED FUNCTION, info:eu-repo/classification/Autores/HYPERSINGULAR, info:eu-repo/classification/cti/7, info:eu-repo/classification/cti/33, |
| Online Access: | http://cicy.repositorioinstitucional.mx/jspui/handle/1003/937 |
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| Summary: | This article considers methods of weakly singular and hypersingular integral regularization based on the theory of distributions. For regularization of divergent integrals, the Gauss–Ostrogradskii theorem and the second Green’s theorem in the sense of the theory of distribution have been used. Equations that allow easy calculation of weakly singular, singular, and hypersingular integrals in one- and two-dimensional cases for any sufficiently smooth function have been obtained. These equations are compared with classical methods of regularization. The results of numerical calculation using classical approaches and those based of the theory of generalized functions, along with a comparison for different functions, are presented in tables and graphs of the values of divergent integrals versus the position of the colocation point. |
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