Approximate methods for solving degenerate singular integral equations 

Il'ya V. Boykov, Doctor of physical and mathematical sciences, professor, professor of the sub-department of higher and applied mathematics, Penza State University
(40 Krasnaya street, Penza, Russia),  i.v.boykov@gmail.com
Anastasiya A. Pivkina, Postgraduate student, Penza State University (40 Krasnaya street, Penza, Russia),  nastyashaldaeva@mail.ru

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.

singular integral equations, degenerate case, Fourier transform, numerical methods

Boykov I.V., Pivkina A.A. Approximate methods for solving degenerate singular integral equations. Izvestiya vysshikh uchebnykh zavedeniy. Povolzhskiy region.
Fiziko-matematicheskie nauki = University proceedings. Volga region. Physical and mathematical sciences. 2023;(1):15–27. (In Russ.). doi: 10.21685/2072-3040-2023-1-2