The Gauss-Legendre rule is very popular in the scalar case, which is due in part to its optimality properties.
The first uses the composite trapezoidal rule and the second the Gauss-Legendre rule.
1/p] by the Gauss-Legendre rule for the integral (2.
2, which evidences once more the good performance of the Gauss-Legendre rule.
The Gauss-Legendre rule has proved to be once more the right choice to work out that approximation.
The same problem occurs with Gauss-Legendre rules, because the estimate (4.
6), a possibility for estimating the number of nodes and weights in Gauss-Legendre rules is by requiring that [parallel]G(2m) - G(m)[parallel] satisfies a prescribed tolerance, where G(m) := [[SIGMA].
7 show respectively for adjacent and common vertex cases, the relative error when calculating the source integral through (9) and the observer integral by means of generalized 2D Cartesian product rules based either on the DE formula or on the Gauss-Legendre rules.
These matrix elements are computed by integrating (9) through 2D generalized Cartesian product rules based on the DE and Gauss-Legendre rules, for levels 0, 1, 2, 3 and 4 in both cases.