Direct and indirect computation of the transport equation eigenvalues

The four most commonly used eigenvalues of the quasi-stationary transport equation are: k, α, γ and δ. Incorporating all these eigenvalues into one equation yields δΩ&oarr;.∇Ψ+ΣΨ+(α/v)Ψ=(S_f/k+S^s)/γ. This equation is solved with one of the eigenvalues `active' while all the other eigenvalues retain their `mute' values (k=1, α=0, γ=1, δ=1). Most computer codes compute directly either the k eigenvalue or the γ eigenvalue. In order to compute α or δ two different approaches are known: the interpolation scheme and the direct scheme. The authors appraise these schemes and show that both can be interpreted as indirect computations utilizing different methods of numerical analysis.