Truncation Error Analysis of Finite Difference Approximations to the Transport Equation

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Abstract
The truncation error of difference approximations to the transport equation is examined, and difference equations which are uniformly second-order accurate are derived. Resulting angular quadrature sets are shown to integrate exactly polynomials of second order in the direction cosines. The analysis is completed for the most general cases of three dimensional spherical and cylindrical geometries. Numerical results comparing this second-order scheme to the standard diamond difference equations in one-dimensional spherical geometry are presented.

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