The ALGORITM EFECTIV PENTRU REZOLVAREA ECUAŢIILOR INTEGRALE SINGULARE

Titu CAPCELEA Catedra Matematica Aplicată

Abstract

We present a fast algorithm with O(n log2 n) computational complexity for the approximate solution of Cauchy 2
singular integral equations with smooth continuous coefficients, defined on the unit circle of the complex plane. In
order to obtain this algorithm we adopt Amosov`s idea [1] to the quadrature method. In the case when the approximate
method is applicable [2], the solution φn of the mentioned fast algorithm satisfies the same convergence rate as the
solution  φ*n of the quadrature method.