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We study the convergence of the discrete ordinates method in the numerical solution of the transport equation for slab geometry. In particular, the combined effect of spatial and angular approximations is analyzed. General conditions are given which guarantee the stability of the combined approximations. Error estimates are derived for both the scalar flux in the Lᵖ-norm, 1 p ∞, and for the approximate critical eigenvalues. A comparison with numerical results indicates that the eigenvalue error estimates are optimal.
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Pitkäranta et al. (1983) studied this question.
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