Numerical quadrature for slab geometry transport algorithms

In recent papers, a generalized nodal finite element formalism has been presented for virtually all known linear finite difference approximations to the discrete ordinates equations in slab geometry. For a particular angular directions μ, the neutron flux Φ is approximated by a piecewise function Oh, which over each space interval can be polynomial or quasipolynomial. Here we shall restrict ourselves to the polynomial case. Over each space interval, Φ is a polynomial of degree k, interpolating parameters given by in the continuous and discontinuous cases, respectively. The angular flux at the left and right ends and the k'th Legendre moment of Φ over the cell considered are represented as