A low memory solver for integral equations of Chandrasekhar type in the radiative transfer problems
type: Item
instance of: scholarly article
title: A low memory solver for integral equations of Chandrasekhar type in the radiative transfer problems
zbMATH Open document ID: 1235.80048
DOI: 10.1155/2011/467017
author: M. Y. Waziri
author: W. J. Leong
author: M. A. Hassan
author: Mansor Monsi
published in: Mathematical Problems in Engineering
publication date: 2012-04-03T00:00:00Z
review text: Summary: The problems of radiative transfer give rise to interesting integral equations that must be faced with efficient numerical solver. Very often the integral equations are discretized to large-scale nonlinear equations and solved by Newton's-like methods. Generally, these kind of methods require the computation and storage of the Jacobian matrix or its approximation. In this paper, we present a new approach that was based on approximating the Jacobian inverse into a diagonal matrix by means of variational technique. Numerical results on well-known benchmarks integral equations involved in the radiative transfer authenticate the reliability and efficiency of the approach. The fact that the proposed method can solve the integral equations without function derivative and matrix storage can be considered as a clear advantage over some other variants of Newton's method.
Mathematics Subject Classification ID: 80M25
Mathematics Subject Classification ID: 80A20
Mathematics Subject Classification ID: 65R20
zbMATH DE Number: 6021097
Wikidata QID: Q58693092
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2011/467017
OpenAlex ID: W2038161960
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description: scientific article; zbMATH DE number 6021097