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An analytical solution for the one-dimensional time-dependent SN transport equation for bounded and unbounded domains in cartesian geometry

C. F. Segatto, M. T. Vilhena and T. T. Gonçalez
From the journal Kerntechnik


In this work a general analytical solution is reported, expressed in integral form for the time-dependent, one-dimensional SN transport equation in cartesian geometry valid for bounded and unbounded domains (0 < x <), using the double Laplace transform technique. The main idea consists in the application of the Laplace transform technique in time variable and the solution of the resulting equation by the LTSN method using appropriate boundary conditions for bounded and unbounded domain problems. We also report about the numerical simulations carried out.


Eine analytische Lösung für die eindimensionale, zeitabhängige SN Transportgleichung für beschränkte und unbeschränkte Gebiete in kartesischer Geometrie. In der vorliegenden Arbeit wird über eine allgemeine analytische Lösung berichtet, ausgedrückt in integraler Form, für die eindimensionale, zeitabhängige SN Transportgleichung in kartesischer Geometrie für beschränkte und unbeschränkte Gebiete (0 < x <) unter Verwendung des Laplace-Transformationsverfahrens. Die grundlegende Idee besteht in der Anwendung des zeitvariablen Laplace-Transformationsverfahrens und der Lösung der resultierenden Gleichungen mit Hilfe der LTSN Methode und geeigneter Randbedingungen für beschränkte und unbeschränkte Gebiete. Über die durchgeführten numerischen Simulationen wird ebenfalls berichtet.

* Universidade Federal do Rio Grande do Sul, Porto Alegre, RS, Brasil. E-mail:


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Received: 2009-6-9
Published Online: 2013-04-05
Published in Print: 2010-03-01

© 2010, Carl Hanser Verlag, München