A Novel Collocation Method for Numerical Solution of Hypersingular Integral Equation with Singular Right-Hand Function

Abstract

In this study, the Fredholm hypersingular integral equation of the first kind with a singular right-hand function on the interval $\left[-1,1\right]$ is solved. The discontinuous solution on the domain $\left[-1,1\right]$ is approximated by a piecewise polynomial, and a collocation method is introduced to evaluate the unknown coefficients. This method, which can be applied to both linear and nonlinear integral equations, is very simple and straightforward. The presented illustrations relate that the results are very accurate compared to the other methods in the literature.