Dual-quadrature representation

In the dual-quadrature representation corresponding to Eq. (3.87), the weights and nodes are neither time-nor space-independent since ka depends on the transported moments. 

Lage, P. L. C. 2011 On the representation of QMOM as a weighted-residual method -the dual-quadrature method of generalized moments. Computers Chemical Engineering 35(11), 2186-2203. 

The convenience of this second case has been noticed by several authors (6-8). The adjoint equation provides an alternative exact representation (dual) for the characteristic. Then, if several values of S are being studied, the effect on N may be computed by quadrature involving only one solution of the adjoint equation. This alternative exact procedure therefore avoids recomputing the equation in N for every S. Thus, Pendlebury (9) Studies the multiplication in a subcritical system as an external source of neutrons impinges at different places on the surface and in doing so has only to solve the (adjoint) transport equation once. 

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