21 January 2009 3:59:14.126 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_o15_x.txt". Quadrature rule W file = "gp_o15_w.txt". Quadrature rule R file = "gp_o15_r.txt". Maximum degree to check = 25 Spatial dimension = 1 Number of points = 15 The quadrature rule to be tested is a Gauss-Legendre rule ORDER = 15 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) = 0.1700171962994026E-01 w( 2) = 0.5160328299707975E-01 w( 3) = 0.9292719531512456E-01 w( 4) = 0.1344152552437842 w( 5) = 0.1715119091363914 w( 6) = 0.2006285293769890 w( 7) = 0.2191568584015875 w( 8) = 0.2255104997982067 w( 9) = 0.2191568584015875 w(10) = 0.2006285293769890 w(11) = 0.1715119091363914 w(12) = 0.1344152552437842 w(13) = 0.9292719531512456E-01 w(14) = 0.5160328299707975E-01 w(15) = 0.1700171962994026E-01 Abscissas X: x( 1) = -0.9938319632127550 x( 2) = -0.9604912687080204 x( 3) = -0.8884592328722570 x( 4) = -0.7745966692414834 x( 5) = -0.6211029467372264 x( 6) = -0.4342437493468025 x( 7) = -0.2233866864289669 x( 8) = 0.000000000000000 x( 9) = 0.2233866864289669 x(10) = 0.4342437493468025 x(11) = 0.6211029467372264 x(12) = 0.7745966692414834 x(13) = 0.8884592328722570 x(14) = 0.9604912687080204 x(15) = 0.9938319632127550 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 = 29 Error Degree 0.0000000000000000 0 0.0000000000000000 1 0.0000000000000002 2 0.0000000000000000 3 0.0000000000000003 4 0.0000000000000000 5 0.0000000000000004 6 0.0000000000000000 7 0.0000000000000004 8 0.0000000000000000 9 0.0000000000000005 10 0.0000000000000000 11 0.0000000000000009 12 0.0000000000000000 13 0.0000000000000008 14 0.0000000000000000 15 0.0000000000000009 16 0.0000000000000000 17 0.0000000000000012 18 0.0000000000000000 19 0.0000000000000013 20 0.0000000000000000 21 0.0000000000000014 22 0.0000000000000000 23 0.0000000674363268 24 0.0000000000000000 25 INT_EXACTNESS_LEGENDRE: Normal end of execution. 21 January 2009 3:59:14.131 PM