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