Annali di Matematica Pura ed Applicata (1923 -)

, Volume 153, Issue 1, pp 229–273 | Cite as

On the convergence of the multigroup, discrete-ordinates solutions for subcritical transport media

  • H. D. VictoryJr.
  • E. J. Allen


In the multigroup, discrete-ordinates approximations to the linear transport equation, the integration over the directional variable is replaced by a numerical quadrature rule, involving a weighted sum over functional values at selected directions, with the energy dependence discretized by replacing the cross section data by weighted averages over each energy interval. The stability, consistency, and convergence rely fundamentally on the conditions that the maximum fluctuations in the total cross section — and in the expected number of secondary particles arising from each energy level — tend to zero as the energy mesh becomes finer, and as the number of angular nodes becomes infinite. Our analysis is based on using a natural Nyström method of extending the discrete-ordinates, multigroup approximates to all values of the angular and energy variables. Such an extension enables us to employ generalizations of the collectively compact operator approximation theory of P. M. Anselone to deduce stability and convergence of the approximates.


Total Cross Section Compact Operator Operator Approximation Secondary Particle Energy Variable 
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.


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Copyright information

© Fondazione Annali di Matematica Pura ed Applicata 1989

Authors and Affiliations

  • H. D. VictoryJr.
    • 1
  • E. J. Allen
    • 1
  1. 1.Institute of Numerical Transport Theory, Department of MathematicsTexas Tech UniversityLubbock

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