On the existence of approximate solution of Fredholm integral equation of the first kind by band-limited scaling function
type: Item
instance of: scholarly article
title: On the existence of approximate solution of Fredholm integral equation of the first kind by band-limited scaling function
zbMATH Open document ID: 1468.45007
author: Gopal Priyadarshi
author: B. V. Rathish Kumar
published in: Differential Equations and Dynamical Systems
publication date: 2021-04-23T00:00:00Z
review text: The authors consider a Fredholm integral equation of the first kind with convolution type kernel of the form \[ \int_{-\infty }^\infty k(x-y)u(y)\,\mathrm{d}y=g(x)\,,\quad x\in \mathbb{R}\,, \] where the kernel \(k\) and the data \(g\) are known functions whereas \(u\) has to be determined. The solution of this integral equation is approximated via band-limited scaling functions generated by a class of band-limited wavelets. Existence and uniqueness of the approximated solution is established and shown to be rapidly converging with a significant reduction in the computational cost. Some numerical results are provided to support their theoretical findings.
reviewed by: Andreas Kleefeld
Mathematics Subject Classification ID: 45L05
Mathematics Subject Classification ID: 45B05
Mathematics Subject Classification ID: 65T60
Mathematics Subject Classification ID: 65R20
zbMATH DE Number: 7336977
zbMATH Keywords: wavelets
zbMATH Keywords: multiresolution analysis
zbMATH Keywords: band-limited scaling function
zbMATH Keywords: integral equation
zbMATH Keywords: Fourier transform
Wikidata QID: Q115376443
MaRDI profile type: Publication
full work available at URL: s12591-018-0416-8
OpenAlex ID: W2796711711
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DOI: 10.1007/S12591-018-0416-8
description: scientific article; zbMATH DE number 7336977