A Method for Accelerating the Iterative Solution of a Class of Fredholm Integral Equations
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.
KeywordsSpectral Radius Iterative Scheme Synthetic Method Iterative Solution Fredholm Integral Equation
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- 1.Kopp, H. J., Synthetic Method Solution of the Transport Equation, Nuclear Science and Engineering, Vol. 17, pp. 65–74, 1963.Google Scholar
- 2.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.Google Scholar
- 3.Wing, G. M., An Introduction to Transport Theory, John Wiley and Sons, New York, New York, 1962.Google Scholar
- 4.Cochran, J. A., Analysis of Linear Integral Equations, McGraw-Hill Publishing Company, New York, New York, 1972.Google Scholar
- 5.Zaanen, A. C., Linear Analysis, John Wiley and Sons (Interscience Publishers), New York, New York, 1953.Google Scholar