A projection method for solving Fredholm integral equations of the second kind
type: Item
instance of: scholarly article
title: A projection method for solving Fredholm integral equations of the second kind
zbMATH Open document ID: 0675.65138
DOI: 10.1016/0168-9274(89)90014-7
author: Hideaki Kaneko
published in: Applied Numerical Mathematics
publication date: 1989-01-01T00:00:00Z
review text: The Fredholm integral equation of the second kind \(x(t)-\int k(t,s)x(s)ds=y(t),\) \(a\leq t\leq b\), is considered. The degenerated kernel methods of approximating the solution of this equation consists of replacing the kernel k(t,s) by a finite rank approximation using bivariate functions. For that purpose a projection of a space of bivariate functions onto its subspace, consisting of functions, each of which is a finite sum of products of univariate functions, is established. These ``basis'' functions can be selected. One can chose them in such a way that the integral can be easy to compute, for example if it refers to the B-spline functions, then the values of such integrals can be used from the tabulograms. Corresponding theorems are presented, proved and used as an example, reducing the problem of constructing projections of univariate functions' spaces.
Mathematics Subject Classification ID: 65R20
Mathematics Subject Classification ID: 45B05
zbMATH DE Number: 4106238
zbMATH Keywords: projection method
zbMATH Keywords: Fredholm integral equation of the second kind
zbMATH Keywords: degenerated kernel methods
zbMATH Keywords: bivariate functions
MaRDI profile type: Publication
full work available at URL: 0168-9274(89)90014-7
OpenAlex ID: W1982161441
cites work: Q4124250
cites work: The Deferred Approach to the Limit for Eigenvalues of Integral Equations
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description: scientific article; zbMATH DE number 4106238