A projection method for solving Cauchy singular integro-differential equations

In this work we present a modified projection method based on Legendre polynomials, for solving integro-differential equations with Cauchy kernel, in L 2 ( [ − 1 , 1 ] , C ) . The proposed numerical procedure leads to solve a system of linear equations. We prove the existence of a solution for the approximate equation, and we perform the error analysis. Numerical examples illustrate the theoretical results.