A Low Memory Solver for Integral Equations of Chandrasekhar Type in the Radiative Transfer Problems. (10th November 2011)

• Record Type: Journal Article
• Authors: Yusuf Waziri, Mohammed; Leong, Wah June; Abu Hassan, Malik; Monsi, Mansor
• Other Names: Mailybaev Alexei Academic Editor.
• Is Part Of: Mathematical problems in engineering. Volume 2011(2011)
• Publication Date: 2011-11-10
• Subjects: Engineering mathematics -- Periodicals; 510.2462
• DOI: 10.1155/2011/467017
• Languages: English
• ISSNs: 1024-123X

Abstract

Abstract : 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.