Convergence of a certain monotone iteration in the reflection matrix for a nonmultiplying half-space
作者:
Paul Nelson,
期刊:
Transport Theory and Statistical Physics
(Taylor Available online 1984)
卷期:
Volume 13,
issue 1-2
页码: 97-106
ISSN:0041-1450
年代: 1984
DOI:10.1080/00411458408211655
出版商: Taylor & Francis Group
数据来源: Taylor
摘要:
A certain monotonically increasing nonlinear iterative procedure, first employed systematically by Shimizu and Aoki, has proven quite effective for computing the reflection matrix for a spatially homogeneous half-space, where the direction and energy variables are treated by suitable discrete approximations. In this paper it is shown that this procedure converges, provided only that the underlying half-space is nonmultiplying. (“Nonmultiplying” means that the maximum expected number of particles emerging from a collision does not exceed unity, where the maximum is taken over all energies and directions of the incident particles.) Furthermore, in this case it is shown that a certain norm of the approximate reflection matrices produced by the iterative process is bounded above by the maximum secondary scattering ratio.
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