Stability analysis of the quasideffusion and second moment methods for iteratively solving discrete-ordinates problems

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Abstract
We consider two previously-published methods for obtaining iterative solutions of discrete-ordinates problems, the nonlinear “quasidiffusion” method developed by Gol'din1, and the “second moment” method proposed by Lewis and Miller2. We describe these methods, show that they reduce to almost the same (linear) method for a special class of problems, and perform a Fourier stability analysis of the two methods for these special problems. This analysis shows that the two methods are stable and rapidly converging for all mesh sizes. We confirm these theoretical predictions by presenting results from direct numerical calculations involving the methods.