22 January 2009 9:22:47.942 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_o1_x.txt". Quadrature rule W file = "leg_o1_w.txt". Quadrature rule R file = "leg_o1_r.txt". Maximum degree to check = 5 Spatial dimension = 1 Number of points = 1 The quadrature rule to be tested is a Gauss-Legendre rule ORDER = 1 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) = 2.000000000000000 Abscissas X: x( 1) = 0.000000000000000 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 = 1 Error Error Degree (This rule) (Trapezoid) 0.0000000000000000 0.0000000000000000 0 0.0000000000000000 0.0000000000000000 1 1.0000000000000000 1.0000000000000000 2 0.0000000000000000 0.0000000000000000 3 1.0000000000000000 1.0000000000000000 4 0.0000000000000000 0.0000000000000000 5 INT_EXACTNESS_LEGENDRE: Normal end of execution. 22 January 2009 9:22:47.944 AM