A stochastic algorithm to solve multiple dimensional Fredholm integral equations of the second kind
type: Item
instance of: scholarly article
title: A stochastic algorithm to solve multiple dimensional Fredholm integral equations of the second kind
zbMATH Open document ID: 1309.65156
author: Rahman Farnoosh
author: Mahboubeh Aalaei
published in: Bulletin of the Iranian Mathematical Society
publication date: 2014-10-22T00:00:00Z
full work available at URL: article 508 62.html
review text: This article focuses on a new stochastic algorithm that is able to solve multiple dimensional Fredholm integral equations of the second kind. The authors describe the solution of the integral equation by a Neumann series expansion. Each term of this series expansion is interpreted as an expectation. The expectation is then approximated by a continuous Markov chain Monte Carlo method. Next, an algorithm is proposed to simulate such a continuous Markov chain with a probability density function that arises from an important sampling technique. The authors establish some theoretical results in a normed space. Precisely, they provide a convergence condition and an error estimation of the new proposed method. It is noteworthy that the method itself has a simple structure and can be easily parallized due to the fact that many independent sample paths are used for estimating the solution. Additionally, numerical results in two dimensions are presented to confirm the efficiency and the accuracy of the new stochastic algorithm.
reviewed by: Andreas Kleefeld
Mathematics Subject Classification ID: 65R20
Mathematics Subject Classification ID: 65C05
Mathematics Subject Classification ID: 45B05
Mathematics Subject Classification ID: 60J22
Mathematics Subject Classification ID: 65C40
zbMATH DE Number: 6359998
zbMATH Keywords: Fredholm integral equations
zbMATH Keywords: continuous Markov chain Monte Carlo method
zbMATH Keywords: convergence
zbMATH Keywords: error estimation
zbMATH Keywords: numerical result
zbMATH Keywords: stochastic algorithm
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 6359998