21 January 2009 3:58:39.647 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_o7_x.txt". Quadrature rule W file = "gp_o7_w.txt". Quadrature rule R file = "gp_o7_r.txt". Maximum degree to check = 12 Spatial dimension = 1 Number of points = 7 The quadrature rule to be tested is a Gauss-Legendre rule ORDER = 7 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) = 0.1046562260264673 w( 2) = 0.2684880898683334 w( 3) = 0.4013974147759622 w( 4) = 0.4509165386584741 w( 5) = 0.4013974147759622 w( 6) = 0.2684880898683334 w( 7) = 0.1046562260264673 Abscissas X: x( 1) = -0.9604912687080204 x( 2) = -0.7745966692414834 x( 3) = -0.4342437493468025 x( 4) = 0.000000000000000 x( 5) = 0.4342437493468025 x( 6) = 0.7745966692414834 x( 7) = 0.9604912687080204 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 = 13 Error Degree 0.0000000000000000 0 0.0000000000000000 1 0.0000000000000002 2 0.0000000000000000 3 0.0000000000000003 4 0.0000000000000000 5 0.0000000000000010 6 0.0000000000000000 7 0.0000000000000011 8 0.0000000000000000 9 0.0000000000000011 10 0.0000000000000000 11 0.0018242388612774 12 INT_EXACTNESS_LEGENDRE: Normal end of execution. 21 January 2009 3:58:39.650 PM