Legendre-collocation method to solve the second kind Cauchy integral equations

A numerical solution for the second kind singular integral equations with Cauchy kernel is developed using the collocation method. To achieve this, we approximate the Cauchy integral equation using the collocation method and Legendre orthogonal polynomial expansions. The accuracy of our proposed method is assessed through convergence and error analysis. Finally, several numerical examples are presented to  demonstrate the high efficiency of the method.

کلیدواژه ها:

Cauchy integral equation ، Legendre polynomials ، collocation method