On approximation and numerical solution of Fredholm integral equations of second kind using quasi-interpolation
type: Item
instance of: scholarly article
title: On approximation and numerical solution of Fredholm integral equations of second kind using quasi-interpolation
zbMATH Open document ID: 1215.65202
author: Frank Müller
author: Werner Varnhorn
published in: Applied Mathematics and Computation
publication date: 2011-03-28T00:00:00Z
review text: The Fredholm integral equation of the second kind \(x-Tx=b\) in Banach space \(C[-1,1]\) is considered. Here \[ T:C[-1,1]\to C[-1,1],\quad (Tx)(s):=\int\limits_{-1}^{1}k(s,t)x(t)dt, \] with continuous kernel \(k:[-1,1]^2\to\mathbb{R}\) and \(b\in C[-1,1]\). The suggested numerical method is based on the approximation of the integral operator \(T\) by quasi-interpolating the density function using Gaussian kernels. The authors show that the approximation of the integral equation, gained with this method, for an appropriate choice of a certain parameter leads to the same numerical results as Nyström's method with the trapezoidal rule. For this, a convergence analysis is carried out. The paper also contains some numerical results illustrating the theoretical estimates.
reviewed by: Alexander N. Tynda
Mathematics Subject Classification ID: 65R20
Mathematics Subject Classification ID: 45B05
Mathematics Subject Classification ID: 45A05
zbMATH DE Number: 5870906
zbMATH Keywords: quasi-interpolation
zbMATH Keywords: Fredholm integral equation
zbMATH Keywords: Gaussian kernels
zbMATH Keywords: Nyström's method
zbMATH Keywords: convergence
zbMATH Keywords: numerical results
MaRDI profile type: Publication
full work available at URL: j.amc.2011.01.022
OpenAlex ID: W1996498115
cites work: Applications of analysis on nilpotent groups to partial differential equations
cites work: Linear integral equations.
cites work: On approximate approximations using Gaussian kernels
cites work: Q3591456
cites work: Error estimates for approximate approximations with Gaussian kernels on compact intervals
cites work: Q4763641
DOI: 10.1016/J.AMC.2011.01.022
description: scientific article; zbMATH DE number 5870906