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 L2([−1,1],C)L2([−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.