Accession Number : ADA301212

Title :   The Mathematical Development of the End-Point Method

Corporate Author : TECHNICAL INFORMATION SERVICE (AEC) OAK RIDGE TN

Personal Author(s) : Frankel, S. ; Goldberg, S.

PDF Url : ADA301212

Report Date : 10 APR 1945

Pagination or Media Count : 48

Abstract : The end-point method is mathematically developed and its application to the Milne kernel studied in detail. The general solution of the Wiener-Hopf integral equation is first obtained. The Mime kernel appears in applying this method to the integral equation describing the diffusion and multiplication of neutrons in multiplying and scattering media. The neutrons are treated as monochromatic, isotropically scattered and of the same total mean free path in all materials involved. Only problems with spherical symmetry are treated, these being reducible to equivalent infinite slab problems. Solutions are obtained for tamped and untamped spheres; in the former case both growing and decaying exponential asymptotic solutions in the tamper are treated in detail. Appendix I treats the effects of the approximations inherent in the end-point method (cf. LADC - 79). Appendix II gives the solution of the inhomogeneous Wiener-Hopf equation. (AN)

Descriptors :   *NUMERICAL METHODS AND PROCEDURES, ONE DIMENSIONAL, KERNEL FUNCTIONS, SOLUTIONS(GENERAL), APPROXIMATION(MATHEMATICS), PARTIAL DIFFERENTIAL EQUATIONS, APPLIED MATHEMATICS, INTEGRAL EQUATIONS, NEUTRONS, ASYMPTOTIC NORMALITY, ANALYTIC FUNCTIONS, LAPLACE TRANSFORMATION, METHOD OF CHARACTERISTICS, MEAN FREE PATH, NEUTRON SCATTERING.

Subject Categories : Numerical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE