A fast algorithm for the numerical solution of an integral equation with logarithmic kernel
type: Item
instance of: scholarly article
title: A fast algorithm for the numerical solution of an integral equation with logarithmic kernel
zbMATH Open document ID: 1349.65659
DOI: 10.2298/PIM1410143F
author: Katharina Flemming
author: Peter Junghanns
publication date: 2016-06-27T00:00:00Z
Mathematics Subject Classification ID: 65N38
Mathematics Subject Classification ID: 65N35
Mathematics Subject Classification ID: 65N20
Mathematics Subject Classification ID: 35J25
Mathematics Subject Classification ID: 65N12
zbMATH DE Number: 6598875
zbMATH Keywords: first kind integral equation
zbMATH Keywords: ill-posed problem
zbMATH Keywords: collocation method
zbMATH Keywords: quadrature method
zbMATH Keywords: boundary integral methods
zbMATH Keywords: algorithm
zbMATH Keywords: convergence
zbMATH Keywords: numerical results
MaRDI profile type: Publication
published in: Publications de l'Institut Mathématique. Nouvelle Série
review text: The authors consider an integral equation problem. Such problems can be related to boundary value partial differential equations -- when boundary integral methods are applied, for instance. An important characteristic of the considered integral operator is that its image is not closed. This yields an ill-posed problem. However, the previous work on this topic shows that, under the suitable assumptions, one can apply a collocation-quadrature method to obtain a convergent sequence of the approximate solutions of this problem. The authors propose an algorithm which provides numerical solution of the considered problem. The main contribution of the presented work is a construction of the algorithm which reduces the complexity of the existing collocation-quadrature method while the same convergence rate is achievable. This results in accelerated algorithm. The presented numerical results show that the proposed scheme produces some significant savings of the CPU-time compared to the existing quadrature method.
description: scientific article; zbMATH DE number 6598875