Efficient methods for Volterra integral equations with highly oscillatory Bessel kernels
type: Item
instance of: scholarly article
title: Efficient methods for Volterra integral equations with highly oscillatory Bessel kernels
zbMATH Open document ID: 1268.65171
author: Shuhuang Xiang
author: H. Brunner
published in: BIT
publication date: 2013-04-03T00:00:00Z
review text: This paper considers Volterra integral equations of the second kind with highly oscillatory weakly singular Bessel kernels. The aim is to provide numerical approximations to the solution. The authors begin by considering the analytical properties of the problem and of its solution before going on to propose an approximation method. They consider a Filon method and two collocation methods based on piecewise constant and piecewise linear functions. An analysis of errors is provided in each case, illustrated by some numerical examples. The authors conclude by summarising how the methods proposed avoid some of the computational costs and pitfalls of alternative approaches.
Mathematics Subject Classification ID: 65R20
Mathematics Subject Classification ID: 45D05
Mathematics Subject Classification ID: 45E10
zbMATH DE Number: 6150057
zbMATH Keywords: Volterra integral equation
zbMATH Keywords: highly oscillatory kernel
zbMATH Keywords: Bessel function kernel
zbMATH Keywords: weak kernel singularity
zbMATH Keywords: Filon method
zbMATH Keywords: collocation method
zbMATH Keywords: numerical examples
reviewed by: Neville J. Ford
MaRDI profile type: Publication
full work available at URL: s10543-012-0399-8
OpenAlex ID: W1989095828
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DOI: 10.1007/S10543-012-0399-8
description: scientific article; zbMATH DE number 6150057