APPROXIMATE SOLUTION OF AN INTEGRAL FIRST-KIND EQUATION WITH THE MULTIPLICATIVE CAUCHY KERNEL BY THE METHOD OF ORTHOGONAL POLYNOMIALS

Abstract

Numerical methods for solving singular integral first-kind equations with a special form of the right-hand side are developed. The proposed schemes are based on the decomposition of singular integrals with power-logarithmic singularity in Chebyshev’s polynomials of first and second kind. Accuracy estimates of the considered methods are presented.