Numerical solution of weakly singular Fredholm integral equations via generalization of the Euler–Maclaurin summation formula

Abstract

Since the classical Euler–Maclaurin summation formula may not be applied for approximating singular integrals, we can not use this formula for obtaining the numerical solution of weakly singular Fredholm integral equations. In this article, we use a generalization of the Euler–Maclaurin summation formula for solving weakly singular Fredholm integral equations of the second kind. By this idea, the basic equations will be changed into the associated systems of algebraic equations. Some numerical examples are given to show the effectiveness of the method.