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Convergence of singular difference approximations for the discrete ordinate equations in $x-y$ geometry

Author: N. K. Madsen
Journal: Math. Comp. 26 (1972), 45-50
MSC: Primary 65N15
MathSciNet review: 0300485
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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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Keywords: Convergence of difference equations, discrete ordinate equations, <IMG WIDTH="52" HEIGHT="37" ALIGN="MIDDLE" BORDER="0" SRC="images/img1.gif" ALT="$x - y$"> geometry, singular difference approximations, diamond difference approximation, central difference approximation, convergence rates
Article copyright: © Copyright 1972 American Mathematical Society