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A posteriori error bounds for numerical solutions of the neutron transport equation


Author: Niel K. Madsen
Journal: Math. Comp. 27 (1973), 773-780
MSC: Primary 82.65
MathSciNet review: 0327236
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Abstract: The theory and application of a method for computing rigorous a posteriori error bounds for numerical solutions to time-independent neutron transport problems are presented. The bounds are obtained for the $ {L_2}$ and $ {L_1}$ norms of the error function.


References [Enhancements On Off] (What's this?)

  • [1] J. Arkuszewski, T. Kulikowska & J. Mika, "Effect of singularities on approximation in $ {S_N}$ methods," Nuclear Sci. Engr., v. 49, 1972, pp. 20-26.
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  • [3] R. B. Kellogg, On the spectrum of an operator associated with the neutron transport equation, SIAM J. Appl. Math. 17 (1969), 162–171. MR 0261813
  • [4] N. K. Madsen, Convergence of Difference Methods for the Linear Transport Equation, Doctoral Dissertation, University of Maryland, College Park, Maryland, 1969.
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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1973-0327236-4
Keywords: A posteriori error bounds, neutron transport equation, linear Boltzmann equation, computable error bounds, $ {L_2}$ error bounds, $ {L_1}$ error bounds, x-y geometry
Article copyright: © Copyright 1973 American Mathematical Society