A numerical algorithm for solving the Cauchy singular integral equation based on Hermite polynomials

Abstract

A numerical algorithm based on Hermite polynomials for solving the Cauchy singular integral equation in the general form is presented. The Hermite polynomial interpolation of unknown functions is first introduced. The proposed technique is then used for approximating the solution of the Cauchy singular integral equation. This approach requires the solution of a system of linear algebraic equations. Two examples demonstrate the effectiveness of the proposed method.