Projection-iterative methods for solving one class of hypersingular integral equations

Title	Projection-iterative methods for solving one class of hypersingular integral equations
Authors	I. V. Boykov¹, P. V. Aykashev¹, A. I. Boykova¹ ¹Penza State University
Annotation	Investigated iterative-projection methods for solving linear and nonlinear hypersingular integral equations of Prandtl's type. We consider the Prandtl equations defined on the segment $ [- 1,1] $ and on the numerical axis $ R_1 = (- \infty, \infty). $ To construct computational schemes, spline-collocation methods with first order splines are used. Justification of the convergence of the proposed computational schemes is based on the continuous method for solving operator equations, which makes it possible to simplify the conditions imposed on the original equation. An additional feature of the continuous operator method is its stability against perturbation of the coefficients and the right-hand sides of the equations.
Keywords	hypersingular integral equations, Prandtl equation, projection methods, iterative methods, continuous operator method
Citation	Boykov I. V., Aykashev P. V., Boykova A. I. ''Projection-iterative methods for solving one class of hypersingular integral equations'' [Electronic resource]. Proceedings of the International Scientific Youth School-Seminar "Mathematical Modeling, Numerical Methods and Software complexes" named after E.V. Voskresensky (Saransk, October 8-11, 2020). Saransk: SVMO Publ, 2020. - pp. 171-178. Available at: https://conf.svmo.ru/files/2020/papers/article05.pdf. - Date of access: 19.04.2024.

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Projection-iterative methods for solving one class of hypersingular integral equations

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