Spectral analysis of numerical methods for discrete-ordinates problems. I

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Abstract
A separation of variable method is proposed for the analysis of spatial differencing schemes for discreate-ordinates problems. This method leads to the defination of a “spectrum” for the differencing scheme which is a function of the cross sections and the spatial mesh. An analysis of the spectrum as a function only of the mesh yields theoretioal results rgarding stability, positivity, and accurancy which have not been obtained previousty. In this paper, we apply the theory to the standard dimond differences scheme and a new extended diamond difference scheme. Numerical results obtained from the solution of discrete-ordinates problems using these two schemes are shown to be in excellent agreement with the spectral theory.