21 January 2009 3:57:56.726 PM
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 = "gp_o3_x.txt".
Quadrature rule W file = "gp_o3_w.txt".
Quadrature rule R file = "gp_o3_r.txt".
Maximum degree to check = 6
Spatial dimension = 1
Number of points = 3
The quadrature rule to be tested is
a Gauss-Legendre rule
ORDER = 3
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) = 0.5555555555555556
w( 2) = 0.8888888888888888
w( 3) = 0.5555555555555556
Abscissas X:
x( 1) = -0.7745966692414834
x( 2) = 0.000000000000000
x( 3) = 0.7745966692414834
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 = 5
Error Degree
0.0000000000000000 0
0.0000000000000000 1
0.0000000000000002 2
0.0000000000000000 3
0.0000000000000003 4
0.0000000000000000 5
0.1599999999999996 6
INT_EXACTNESS_LEGENDRE:
Normal end of execution.
21 January 2009 3:57:56.729 PM