Airfoil polynomials for solving integro-differential equations with logarithmic kernel

摘要

In this paper we introduce a collocation method, for approximate solution of an integro-differential equations with logarithmic kernel, using airfoil polynomials. We prove the existence of the solution for the approximate equation, and we perform the error analysis. A system of linear equations is to be solved. Finally, some numerical examples illustrate the accuracy of the method.