SOLUTION OF SOME SINGULAR INTEGRAL EQUATIONS BY MEANS OF ASYMPTOTIC POLYNOMIALS

Abstract

The paper proposes a new method for approximate solution of singular integral equations with the Cauchy-type kernel which are taken along the real axis segment. Integration function can be represented as an asymptotic polynomial or infinite series using the Chebyshev polynomials. The remainder has been obtained simultaneously with the approximate solution. Its form makes it possible to determine degree of the polynomial that provides an approximate solution with a given accuracy.