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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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Convergence of singular difference approximations for the discrete ordinate equations in $x-y$ geometry
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by N. K. Madsen PDF
Math. Comp. 26 (1972), 45-50 Request permission

Abstract:

The solutions to two well-known finite difference approximations are shown to converge to the solution of the discrete ordinate equations which are an approximation to the linear Boltzmann equation. These difference schemes are the diamond approximation of Carlson, and the central difference approximation. These schemes are known to give singular systems of algebraic equations in certain cases. Despite this singularity, convergence is shown for all cases when solutions exist.
References
  • B. Davison and J. B. Sykes, Neutron transport theory, Oxford, at the Clarendon Press, 1957. MR 0095716
  • G. C. Wick, Über ebene Diffusions-probleme, Z. Phys. 121 (1943), 702–718 (German). MR 0010052, DOI 10.1007/BF01339167
  • S. Chandrasekhar, On the radiative equilibrium of a stellar atmosphere. II, Astrophys. J. 100 (1944), 76–86. MR 10831, DOI 10.1086/144639
  • Herbert B. Keller, On the pointwise convergence of the discrete-ordinate method, J. Soc. Indust. Appl. Math. 8 (1960), 560–567. MR 169388, DOI 10.1137/0108042
  • Burton Wendroff, On the convergence of the discrete ordinate method, J. Soc. Indust. Appl. Math. 8 (1960), 508–513. MR 128636, DOI 10.1137/0108034
  • N. K. Madsen, Pointwise convergence of the three-dimensional discrete ordinate method, SIAM J. Numer. Anal. 8 (1971), 266–269. MR 285151, DOI 10.1137/0708027
  • Bengt G. Carlson, The numerical theory of neutron transport, Methods in Computational Physics, Vol. 1, Academic Press, New York, 1963, pp. 1–42. MR 0155448
  • N. K. Madsen, Convergence of Difference Methods for the Linear Transport Equation, Doctoral Dissertation, University of Maryland, College Park, Md., 1969. J. A. Davis, L. A. Hageman & R. B. Kellogg, “Singular difference approximations for the discrete ordinate equations in $x - y$ geometry,” Nuclear Sci. Eng., v. 29, 1967, pp. 237-243.
  • E. M. Gelbard, James A. Davis, and L. A. Hageman, Solution of the discrete ordinate equations in one and two dimensions. , Transport Theory (Proc. Sympos. Appl. Math., New York, 1967) Amer. Math. Soc., Providence, R.I., 1969, pp. 129–158. MR 0277118
  • R. B. Kellogg, On the spectrum of an operator associated with the neutron transport equation, SIAM J. Appl. Math. 17 (1969), 162–171. MR 261813, DOI 10.1137/0117015
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Additional Information
  • © Copyright 1972 American Mathematical Society
  • Journal: Math. Comp. 26 (1972), 45-50
  • MSC: Primary 65N15
  • DOI: https://doi.org/10.1090/S0025-5718-1972-0300485-6
  • MathSciNet review: 0300485