Numerical solution of various cases of Cauchy type singular integral equation

Abstract

In this paper, a robust but very simple numerical method is developed to solve various cases of Cauchy type singular integral equation. For this, first Bernstein polynomials are defined which are used for approximation of solution of the given singular integral equation. Then numerical method is introduced by using Bernstein polynomials. This ultimately leads to solution of a system of linear algebraic equations. Examples are illustrated to demonstrate simplicity of proposed method. Results are also compared with those present in literature to claim better efficiency of the method introduced.