Approximate methods for solving degenerate singular integral equations
Background. Singular integral equations in degenerate cases describe many processes in natural science and technology. The theory of these equations has been studied quite well, but as far as the authors know, there are currently no analytical methods for solving them. In this regard, there is a nee...
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| Format: | Article |
| Language: | English |
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Penza State University Publishing House
2023-08-01
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| Series: | Известия высших учебных заведений. Поволжский регион: Физико-математические науки |
| Subjects: |
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| author | Il'ya V. Boykov Anastasiya A. Pivkina |
| author_facet | Il'ya V. Boykov Anastasiya A. Pivkina |
| author_sort | Il'ya V. Boykov |
| collection | DOAJ |
| description | Background. Singular integral equations in degenerate cases describe many processes in natural science and technology. The theory of these equations has been studied quite well, but as far as the authors know, there are currently no analytical methods for solving them. In this regard, there is a need to construct approximate methods for solving singular integral equations in degenerate cases. The article is devoted to the construction of such methods, which determines its relevance. Materials and methods. When constructing approximate methods, iteration-projection methods are used. Results and conclusions. A spline-collocation method for solving a degenerate singular characteristic equation is constructed. A two-stage approximate method is proposed for solving complete singular integral equations in degenerate cases and their characteristic equations. |
| first_indexed | 2024-03-12T14:08:26Z |
| format | Article |
| id | doaj.art-1c038d8825ab4160bbeee05de613c889 |
| institution | Directory Open Access Journal |
| issn | 2072-3040 |
| language | English |
| last_indexed | 2024-03-12T14:08:26Z |
| publishDate | 2023-08-01 |
| publisher | Penza State University Publishing House |
| record_format | Article |
| series | Известия высших учебных заведений. Поволжский регион: Физико-математические науки |
| spelling | doaj.art-1c038d8825ab4160bbeee05de613c8892023-08-21T10:43:53ZengPenza State University Publishing HouseИзвестия высших учебных заведений. Поволжский регион: Физико-математические науки2072-30402023-08-01110.21685/2072-3040-2023-1-2Approximate methods for solving degenerate singular integral equations Il'ya V. Boykov0Anastasiya A. Pivkina1Penza State UniversityPenza State UniversityBackground. Singular integral equations in degenerate cases describe many processes in natural science and technology. The theory of these equations has been studied quite well, but as far as the authors know, there are currently no analytical methods for solving them. In this regard, there is a need to construct approximate methods for solving singular integral equations in degenerate cases. The article is devoted to the construction of such methods, which determines its relevance. Materials and methods. When constructing approximate methods, iteration-projection methods are used. Results and conclusions. A spline-collocation method for solving a degenerate singular characteristic equation is constructed. A two-stage approximate method is proposed for solving complete singular integral equations in degenerate cases and their characteristic equations.singular integral equationsdegenerate casefourier transformnumerical methods |
| spellingShingle | Il'ya V. Boykov Anastasiya A. Pivkina Approximate methods for solving degenerate singular integral equations Известия высших учебных заведений. Поволжский регион: Физико-математические науки singular integral equations degenerate case fourier transform numerical methods |
| title | Approximate methods for solving degenerate singular integral equations |
| title_full | Approximate methods for solving degenerate singular integral equations |
| title_fullStr | Approximate methods for solving degenerate singular integral equations |
| title_full_unstemmed | Approximate methods for solving degenerate singular integral equations |
| title_short | Approximate methods for solving degenerate singular integral equations |
| title_sort | approximate methods for solving degenerate singular integral equations |
| topic | singular integral equations degenerate case fourier transform numerical methods |
| work_keys_str_mv | AT ilyavboykov approximatemethodsforsolvingdegeneratesingularintegralequations AT anastasiyaapivkina approximatemethodsforsolvingdegeneratesingularintegralequations |