On a new computational solution of time-dependent processes-I: a one-dimensional case.
Purchase Print Copy
|Add to Cart||Paperback8 pages||$15.00||$12.00 20% Web Discount|
A discussion of the transformation of linear functional equations subject to boundary conditions into nonlinear functional equations subject only to initial conditions in space and time coordinates. The approach of invariant imbedding yields the reflected and transmitted fluxes as functions of basic physical dimensions. The computational treatment of the reflection of plane parallel flux form an infinite plane medium of finite thickness has already been determined for the steady state-case. As a first step toward the computational solution of the corresponding problem for the time-dependent case, this paper studies the reflected flux from a one-dimensional rod for the case of neutron transport. To obtain a numerical solution, the problem of inverting the Laplace transform numerically is investigated. The method used is quite simple and is applicable to more general problems.
This report is part of the RAND Corporation Paper series. The paper was a product of the RAND Corporation from 1948 to 2003 that captured speeches, memorials, and derivative research, usually prepared on authors' own time and meant to be the scholarly or scientific contribution of individual authors to their professional fields. Papers were less formal than reports and did not require rigorous peer review.
This document and trademark(s) contained herein are protected by law. This representation of RAND intellectual property is provided for noncommercial use only. Unauthorized posting of this publication online is prohibited; linking directly to this product page is encouraged. Permission is required from RAND to reproduce, or reuse in another form, any of its research documents for commercial purposes. For information on reprint and reuse permissions, please visit www.rand.org/pubs/permissions.
The RAND Corporation is a nonprofit institution that helps improve policy and decisionmaking through research and analysis. RAND's publications do not necessarily reflect the opinions of its research clients and sponsors.