Abstract:Background. The numerical method for solving hypersingular integral equations on a segment that arise in many problems of mathematical physics is considered. Materials and methods. Galerkin method is used to solve hypersingular equations with basic functions - Chebyshev polynomials of the 2${}$ kind. The projection method is considered in special classes of functions. Results and conclusions. The convergence of Galerkin method for solving hypersyngular equations in special classes of functions is proved. An estimate of the convergence rate of Galerkin method is obtained.
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