ALGORITM EFECTIV PENTRU REZOLVAREA ECUAŢIILOR INTEGRALE SINGULARE

Abstract

We present a fast algorithm with O(n log 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 n ∗ ϕ of the quadrature method.