On the numerical solution of integral equations with piecewise continuous displacement kernels
type: Item
instance of: scholarly article
title: On the numerical solution of integral equations with piecewise continuous displacement kernels
zbMATH Open document ID: 0726.65151
DOI: 10.1007/BF01199457
author: I. Gohberg
author: I. Koltracht
author: P. Lancaster
published in: Integral Equations and Operator Theory
publication date: 1989-01-01T00:00:00Z
review text: The authors give the solution of the equation \(x(t)-\int^{T}_{0}k(t- r)x(r)dr=f(t),\) \(0\leq t\leq T\), where k(t) is a piecewise continuous \(p\times p\) matrix valued kernel and f(t) is a piecewise continuous p vector valued function, and prove that it is equivalent to the solution of an initial value problem for a partial differential equation. A difference scheme for the last problem is derived and compared with a corresponding quadrature method.
Mathematics Subject Classification ID: 65R20
Mathematics Subject Classification ID: 65M06
Mathematics Subject Classification ID: 65Y05
Mathematics Subject Classification ID: 45B05
zbMATH DE Number: 4199581
zbMATH Keywords: Fredholm integral equations
zbMATH Keywords: displacement kernel
zbMATH Keywords: difference scheme
zbMATH Keywords: initial value problem
zbMATH Keywords: parallel processors
zbMATH Keywords: linear complexity
zbMATH Keywords: quadrature method
zbMATH Keywords: comparison of methods
zbMATH Keywords: piecewise continuous
reviewed by: Chuangan Hu
MaRDI profile type: Publication
cites work: Numerical solution of integral equations, fast algorithms and Krein- Sobolev equation
cites work: Second order parallel algorithms for Fredholm integral equations with continuous displacement kernels
cites work: Linear complexity parallel algorithms for linear systems of equations with recursive structure
full work available at URL: https://doi.org/10.1007/bf01199457
OpenAlex ID: W2041971422
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description: scientific article; zbMATH DE number 4199581