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Asymptotic solution of critical thickness with direct second kind Chebyshev polynomial approximation in forward and backward scattering

Asymptotische Lösung der kritischen Dicke mit Hilfe von Tschebyscheff-Polynomen zweiter Art bei Vorwärts- und Rückwärtsstreuung
F. Yaşa
From the journal Kerntechnik

Abstract

To develop a model with scattering medium, a consistent backward forward scattering kernel is described and applied to the transport equation in plane geometry. Asymptotic solutions of critical half thicknesses are computed by using the direct second kind Chebyshev polynomial method (UN).

Kurzfassung

Zur Entwicklung eines Modells mit Streumedium wird ein konsistenter Rückwärts-Vorwärts-Streukern beschrieben und angewendet auf die Transportgleichung in ebener Geometrie. Asymptotische Lösungen kritischer Halbwertsdicken werden berechnet mit Hilfe der Methode der direkten Tschebyscheff-Polynome zweiter Art (UN).

References

1 Inönü, E.: A theorem on anisotropic scattering. Transp. Theory and Stat. Phys.31 (1973) 137 Search in Google Scholar

2 Conkie, W. R.: Polynomial approximations in neutron transport theory. Nuclear Science and Engineering6 (1959) 260 Search in Google Scholar

3 Yabushita, S.: Tschebyscheff polynomial approximation method of the neutron-transport equationJ. of Math. Phys2 (1961) 543 Search in Google Scholar

4 Anlı, F.; Yaşa, F.; Güngör, S.; Öztürk, H.: TN approximation to neutron transport equation and application to critical slab problem. J. Quant. Spectrosc. Radiat. Transfer101 (2006) 129 Search in Google Scholar

5 Asadzadeh, M.; Kadem, A.: Chebyshev spectral SN method for the neutron transport equation. Computer and Mathematics with Applications52 (2006) 509 10.1016/j.camwa.2005.11.039 Search in Google Scholar

6 Öztürk, H.: The reflected critical slab problem for one-speed neutrons with strongly anisotropic scattering. Kerntechnik73 (2008) 66 Search in Google Scholar

7 Yilmazer, A.; Tombakoglu, M.: On equiconvergence of ultraspherical polynomials, solution of one-speed neutron transport equation. Ann. Nucl. Energy33 (2007) 957 Search in Google Scholar

Received: 2009-11-23
Published Online: 2013-04-05
Published in Print: 2010-08-01

© 2010, Carl Hanser Verlag, München