Recursive generation of the Galerkin-Chebyshev matrix for convolution kernels
type: Item
instance of: scholarly article
title: Recursive generation of the Galerkin-Chebyshev matrix for convolution kernels
zbMATH Open document ID: 0922.65095
DOI: 10.1023/A:1018933305810
author: Davis K. Cope
published in: Advances in Computational Mathematics
publication date: 1999-05-31T00:00:00Z
review text: Today integral equations play a very vital part in formulating, analyzing and solving many practical problems in science, engineering and technology. The computational aspects of solutions are often quite complicated. By careful handling of inputs in explicit situations, however, we can arrive at satisfactory results. The present paper is concerned with integral equations of the first kind having convolution forms in a finite interval. A Galerkin-Chebyshev (G-C) procedure applying to Galerkin's method to the convolution integral \[ \int^1_{-1} K(x-y) g(y)dy= f(x)\quad (-1<x<+1) \] is discussed. Through one basic theorem a general recursion relation for the G-C-matrix components is obtained. Result for the fast generation of the G-C-matrix \(K_{m,n}\) for special convolution kernels are presented and extended to additional recursion relations. A lemma and two more theorems are given on similar lines with proofs. In a numerical examples, the author considers the calculation of G-C-matrix entries \(L^{(0,\sigma)}_{m,n}\) for \(0\leq m\leq M\), \(0\leq n\leq N\) for the modified Bessel function kernel \(K_0(\sigma lx-yl)\). Eleven references are provided.
Mathematics Subject Classification ID: 65R20
Mathematics Subject Classification ID: 45E10
zbMATH DE Number: 1279274
zbMATH Keywords: convolution kernels
zbMATH Keywords: Galerkin-Chebyshev method
zbMATH Keywords: finite interval
zbMATH Keywords: numerical examples
zbMATH Keywords: Bessel function kernel
MaRDI profile type: Publication
full work available at URL: a:1018933305810
OpenAlex ID: W153536122
description: scientific article; zbMATH DE number 1279274