The numerical treatment of Love's integral equation having very small parameter
type: Item
instance of: scholarly article
title: The numerical treatment of Love's integral equation having very small parameter
zbMATH Open document ID: 1232.65187
author: Pietro Pastore
published in: Journal of Computational and Applied Mathematics
publication date: 2011-12-21T00:00:00Z
review text: The author investigates the numerical solution of Love's integral equation \[ f(y)+ {1\over\pi}\int_{-1}^1{c\over{(x-y)^2+c^2}}f(x)\text{d}x=1, |y|\leq 1, 0\leq c\in\mathbb{R} \] with the parameter \(c\) using a stable and convergent method based on the paper of \textit{M. C. De Bonis} and \textit{P. Pastore} [``A quadrature formula for integrals of highly oscillatory functions'', Rend. Circ. Mat. Palermo (2), Suppl., 82, 279--303 (2010)].
Mathematics Subject Classification ID: 65R20
Mathematics Subject Classification ID: 45B05
zbMATH DE Number: 5991195
zbMATH Keywords: Love's integral equation
zbMATH Keywords: system of Fredholm integral equations
zbMATH Keywords: Nyström method
zbMATH Keywords: Gaussian quadrature rule
zbMATH Keywords: condition number
zbMATH Keywords: Toeplitz matrix
reviewed by: Chuangan Hu
MaRDI profile type: Publication
full work available at URL: j.cam.2011.08.011
OpenAlex ID: W2061214985
cites work: Q3383451
cites work: The Numerical Solution of Fredholm integral Equations of the Second Kind
cites work: Algebraic methods for Toeplitz-like matrices and operators
cites work: Q4337625
cites work: THE ELECTROSTATIC FIELD OF TWO EQUAL CIRCULAR CO-AXIAL CONDUCTING DISKS
cites work: The numerical solution of non-singular linear integral equations
cites work: The application of approximate product-integration to the numerical solution of integral equations
cites work: A Chebyshev series method for the numerical solution of Fredholm integral equations
cites work: The numerical solution of non-singular integral and integro-differential equations by iteration with Chebyshev series
cites work: Chebyshev Solution of Differential, Integral and Integro-Differential Equations
cites work: The Use of Collocation as a Projection Method for Solving Linear Operator Equations
cites work: Numerical solution of non-singular Fredholm integral equations of the second kind
cites work: Q3801028
cites work: Q4429496
cites work: Q4917542
DOI: 10.1016/J.CAM.2011.08.011
description: scientific article; zbMATH DE number 5991195