On the uniform convergence of the method of waveletquadratures for the solution of a singular integral equation of the first kind

Abstract

© 2019 IOP Publishing Ltd. We propose a method of wavelet-quadratures for the solution of a singular integral equation of the first kind with a Cauchy kernel on a segment of the real axis, which is a mathematical model of many applied problems. To solve this equation, a computational scheme is constructed, based on the approximation of the unknown function by Chebyshev wavelets of the second kind and using the quadrature Gauss formula. Uniform estimates of the error of approximate solutions are obtained, which take into account the structural properties of the initial data. A numerical experiment was carried out using the Wolfram Mathematica package.