A projection method with smoothing transformation for second kind volterra integral equations

Fermo L.

;Occorsio D.

2021-01-01

---

Abstract

In this paper we present a projection method for linear second kind Volterra integral equations with kernels having weak diagonal and/or boundary singularities of algebraic type. The proposed approach is based on a specific optimal interpolation process and a smoothing transformation. The convergence of the method is proved in suitable spaces of functions, equipped with the uniform norm. Several tests show the accuracy of the presented method.