Analytic Solution of the SN Equations by Integral Transform Technique

  • Marco T. Vilhena
  • Haroldo F. de Campos Velho
  • Cynthia F. Segatto
  • Glênio A. Gonçalves


The LTSN method that appeared in the last decades [1, 2], solves the dicrete ordinates equations (SN equations) by the Laplace transform technique in a slab. The main idea is: (i) application of the Laplace transform to the set of SN equations, (ii) analytical solution of the resulting linear system depending on the complex parameter s, and (iii) analytic inversion of the transformed angular flux. The convergence of the LTSJV method was proved in the framework of C0-semigroup theory [3].


Cylindrical Geometry Transport Problem Isotropic Scattering Analytic Inversion Result Linear System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    M.T. Vilhena and L.B. Barichello, An analytical solution for the multigroup slab geometry discrete ordinates problems, Transport Theor. Stat. 224 (1995), 1337–1352.CrossRefGoogle Scholar
  2. 2.
    C.F. Segatto and M.T. Vilhena, State-of-art of the LTSN method, in Mathematics and Computation, Reactor Physics and Environmental Analysis in Nuclear Applications, Proc. of M&C‘99‚ J.M. Aragonés, C. Ahnert, and O. Cabellos (eds.), Senda Editorial, Madrid, 1618–1631, 1999.Google Scholar
  3. 3.
    M.T. Vilhena and R.P. Pazos, Convergence in transport theory, Appl. Numer. Math. 30 (1999), 79–92.MathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    G. J. Mitisis, Transport Solutions to the Monoenergetic Critical Problems, PhD Thesis, Report ANL-6787, Argone National Laboratory, Chicago, 1963.CrossRefGoogle Scholar
  5. 5.
    R. Piessens, The Hankel transform, in The Transforms and Applications Handbook, 2nd ed., A. Poularikas (ed.), CRC Press, 1996.Google Scholar
  6. 6.
    I.N. Sneddon, The Use of Integral Transforms, MacGraw-Hill, 1972.Google Scholar
  7. 7.
    Bateman manuscript project, in Tables of Integral Transforms, vol. II, McGraw-Hill, 1954.Google Scholar
  8. 8.
    C.E. Siewert and R.J. Thomas, Jr., Neutron transport calculations in cylindrical geometry, Nuclear Sci. Engrg. 87 (1984), 107–112.Google Scholar
  9. 9.
    R.P. Pazos, M.T. Vilhena, and E.B. Häuser, Solution and study of two-dimensional nodal neutron transport equation, Tenth International Conference on Nuclear Engineering ICONE 10, Arlington, 2002.Google Scholar

Copyright information

© Springer Science+Business Media New York 2004

Authors and Affiliations

  • Marco T. Vilhena
  • Haroldo F. de Campos Velho
  • Cynthia F. Segatto
  • Glênio A. Gonçalves

There are no affiliations available

Personalised recommendations