Quadrature Lobatto

No readily useful analytical solutions are available for the system (7) and we resort to an expansion of the amplitude functions in a basis set. The discrete variable representation is a convenient means and we chose to employ a localized basis associated with the Lobatto quadrature rule. It is convenient then to choose units and displacement such that the interval [r,p] equals the standard one, [-1,1]. A basis of n+1 Lagrange interpolation functions is defined from the Legendre polynomial Pniq) as follows... 

Some recent Runge-Kutta formulae are based on quadrature methods, that is, the points at which the intermediate stage approximations are taken are the same points used in integration with either Gauss or Lobatto or Radau rules (Chapter 1). For example, the Runge-Kutta method derived from the Lobatto quadrature with three points (also called the Cavalieri-Simpson rule) is... 

The last section illustrated the Radau quadrature formula when one of the quadrature points is on the boundary either at a = 0 or a = 1. In this section, we present the Lobatto quadrature formula, which includes both boundary points in addition to the N interior quadrature points. The general formula for the Lobatto quadrature is... 

Table E.8 Quadrature Points and Weijd>ts for Lobatto Quadrature Weighting Function FF(x) = 1...

Table E.9 Quadrature Points and Weights for Lobatto Quadrature Weighting Function W(jc) = jc (l - x) ...

Table E.8 lists values of quadrature points and weights for the Lobatto quadrature formula.

The angular flux spectrum was computed using the DTF-IV code in an approximation (Lobatto quadrature) to the transport equation. The GAM-]1 code was used to obtain 27-group, P, cross sections Cor the constituents of the subcritical assembly. Energy self-shielding calculations for were performed with the... 

Matrix in Golub-Welsch algorithm for which the eigensys-tem are the Gauss-Lobatto quadrature points and weights Product difference matrix of order (2Nq- -l)(2Nq- -l) in PD algorithm... 

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