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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

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

The 2020 MCQ for Mathematics of Computation is 1.78.

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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.
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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