Abstract
The present paper extends the synthetic method of transport theory to a large class of integral equations. Convergence and divergence properties of the algorithm are studied analytically, and numerical examples are presented which demonstrate the expected theoretical behavior. It is shown that, in some instances, the computational advantage over the familiar Neumann approach is substantial.
Similar content being viewed by others
References
Kopp, H. J.,Synthetic Method Solution of the Transport Equation, Nuclear Science and Engineering, Vol. 17, pp. 65–74, 1963.
Cesari, L.,Sulla Risoluzione dei Sistemi di Equazioni Lineari par Approsimazioni Successive, Atti della Accademia Nationale dei Lincei, Rendiconti della Classe di Scienze, Fisiche, Matematiche, e Naturali, Vol. 25, pp. 422–428, 1937.
Wing, G. M.,An Introduction to Transport Theory, John Wiley and Sons, New York, New York, 1962.
Cochran, J. A.,Analysis of Linear Integral Equations, McGraw-Hill Publishing Company, New York, New York, 1972.
Zaanen, A. C.,Linear Analysis, John Wiley and Sons (Interscience Publishers), New York, New York, 1953.
Author information
Authors and Affiliations
Additional information
Communicated by M. A. Golberg
This authors acknowledge with pleasure conversations with Paul Nelson. Thanks are due also to Janet E. Wing, whose computer program was used in making the calculations reported in Section 8.
This work was performed in part under the auspices of USERDA at the Los Alamos Scientific Laboratory of the University of California, Los Alamos, New Mexico.
Rights and permissions
About this article
Cite this article
Allen, R.C., Wing, G.M. A method for accelerating the iterative solution of a class of Fredholm integral equations. J Optim Theory Appl 24, 5–27 (1978). https://doi.org/10.1007/BF00933180
Issue Date:
DOI: https://doi.org/10.1007/BF00933180