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

DOI:
https://doi.org/10.1090/S0025-5718-1973-0327236-4

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 and norms of the error function.

**[1]**J. Arkuszewski, T. Kulikowska & J. Mika, "Effect of singularities on approximation in methods,"*Nuclear Sci. Engr.*, v. 49, 1972, pp. 20-26.**[2]**B. Davison and J. B. Sykes,*Neutron transport theory*, Oxford, at the Clarendon Press, 1957. MR**0095716****[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**, https://doi.org/10.1137/0117015**[4]**N. K. Madsen,*Convergence of Difference Methods for the Linear Transport Equation*, Doctoral Dissertation, University of Maryland, College Park, Maryland, 1969.**[5]**M. Natelson, "A strategy for the application of space-angle synthesis to practical problems in neutron transport,"*Nuclear Sci.. Engr.*, v. 31, 1968, pp. 325-336.**[6]**V. S. Vladimirov,*Mathematical Problems in the One-Velocity Theory of Particle Transport*, AECL-1661, Atomic Energy of Canada, Ltd., Chalk River, Ontario, 1963.

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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,
error bounds,
error bounds,
*x-y* geometry

Article copyright:
© Copyright 1973
American Mathematical Society