22 January 2009 9:22:55.411 AM
INT_EXACTNESS_LEGENDRE
FORTRAN90 version
Investigate the polynomial exactness of a Gauss-Legendre
quadrature rule by integrating weighted
monomials up to a given degree over the [-1,+1] interval.
INT_EXACTNESS_LEGENDRE: User input:
Quadrature rule X file = "leg_o2_x.txt".
Quadrature rule W file = "leg_o2_w.txt".
Quadrature rule R file = "leg_o2_r.txt".
Maximum degree to check = 5
Spatial dimension = 1
Number of points = 2
The quadrature rule to be tested is
a Gauss-Legendre rule
ORDER = 2
Standard rule:
Integral ( -1 <= x <= +1 ) f(x) dx
is to be approximated by
sum ( 1 <= I <= ORDER ) w(i) * f(x(i)).
Weights W:
w( 1) = 0.9999999999999998
w( 2) = 0.9999999999999998
Abscissas X:
x( 1) = -0.5773502691896257
x( 2) = 0.5773502691896257
Region R:
r( 1) = -1.0000000000000000
r( 2) = 1.0000000000000000
A Gauss-Legendre rule would be able to exactly
integrate monomials up to and including degree = 3
Error Error Degree
(This rule) (Trapezoid)
0.0000000000000002 0.0000000000000000 0
0.0000000000000000 0.0000000000000000 1
0.0000000000000002 2.0000000000000004 2
0.0000000000000000 0.0000000000000000 3
0.4444444444444446 4.0000000000000000 4
0.0000000000000000 0.0000000000000000 5
INT_EXACTNESS_LEGENDRE:
Normal end of execution.
22 January 2009 9:22:55.413 AM