Mathematical Problems in Engineering
Volume 2011 (2011), Article ID 467017, 12 pages
Research Article

A Low Memory Solver for Integral Equations of Chandrasekhar Type in the Radiative Transfer Problems

Department of Mathematics, Faculty of Science, Universiti Putra Malaysia, 43400 Serdang, Malaysia

Received 4 February 2011; Revised 14 July 2011; Accepted 8 August 2011

Academic Editor: Alexei Mailybaev

Copyright © 2011 Mohammed Yusuf Waziri et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.