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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- © 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