A collocation method for weakly singular integral equations with super-algebraic convergence rate
type: Item
instance of: scholarly article
title: A collocation method for weakly singular integral equations with super-algebraic convergence rate
zbMATH Open document ID: 1356.65249
author: Tilo Arens
author: Thomas Rösch
published in: Numerische Mathematik
publication date: 2016-12-20T00:00:00Z
review text: The paper explores collocation schemes based on trigonometric polynomials for the numerical solution of biperiodic weakly singular integral equations of the second kind. The approach uses a co-ordinate transformation to remove the singularity and a discretisation based on the product trapezoidal scheme. Stability and convergence results are provided under regularity assumptions and the results are compared to actual practical examples where numerical examples are used to demonstrate that the high convergence rates predicted by the theory can be achieved in realistic problems. As the authors point out in their introduction, the method has to compete with simpler strategies that achieve \(4\)th-order convergence by neglecting the singularity in a clever way. The examples and the authors' conclusions demonstrate that their approach competes effectively.
Mathematics Subject Classification ID: 65R20
Mathematics Subject Classification ID: 45E10
zbMATH DE Number: 6666240
zbMATH Keywords: trapezoidal rule
zbMATH Keywords: collocation method
zbMATH Keywords: biperiodic weakly singular integral equations of the second kind
zbMATH Keywords: stability
zbMATH Keywords: convergence
zbMATH Keywords: numerical example
reviewed by: Neville J. Ford
MaRDI profile type: Publication
full work available at URL: s00211-015-0783-9
OpenAlex ID: W2287401681
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DOI: 10.1007/S00211-015-0783-9
description: scientific article; zbMATH DE number 6666240