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

Authors : Behrouz PARSA MOGHADDAM, J A TENREİRO MACHADO, Parisa SATTARİ SHAJARİ, Zeynab SALAMAT MOSTAGHİM

Pages : 974-983

Doi:10.15672/hujms.474938

View : 22 | Download : 8

Publication Date : 2020-06-02

Article Type : Research Paper

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.
Keywords : Cauchy singular integral equation, Hermite polynomials, Numerical schemes, Interpolation theory