25 February 2008 4:56:14.023 PM INT_EXACTNESS_GEGENBAUER FORTRAN90 version Investigate the polynomial exactness of a Gauss-Gegenbauer quadrature rule by integrating weighted monomials up to a given degree over the [-1,+1] interval. INT_EXACTNESS_GEGENBAUER: User input: Quadrature rule X file = "gegen_o8_a0.5_x.txt". Quadrature rule W file = "gegen_o8_a0.5_w.txt". Quadrature rule R file = "gegen_o8_a0.5_r.txt". Maximum degree to check = 19 Exponent of (1-x^2), ALPHA = 0.500000 Spatial dimension = 1 Number of points = 8 The quadrature rule to be tested is a Gauss-Gegenbauer rule ORDER = 8 ALPHA = 0.500000 Standard rule: Integral ( -1 <= x <= +1 ) (1-x^2)^alpha f(x) dx is to be approximated by sum ( 1 <= I <= ORDER ) w(i) * f(x(i)). Weights W: w( 1) = 0.4083294770910693E-01 w( 2) = 0.1442256007956728 w( 3) = 0.2617993877991495 w( 4) = 0.3385402270935191 w( 5) = 0.3385402270935191 w( 6) = 0.2617993877991495 w( 7) = 0.1442256007956728 w( 8) = 0.4083294770910754E-01 Abscissas X: x( 1) = -0.9396926207859084 x( 2) = -0.7660444431189780 x( 3) = -0.5000000000000000 x( 4) = -0.1736481776669303 x( 5) = 0.1736481776669303 x( 6) = 0.5000000000000000 x( 7) = 0.7660444431189780 x( 8) = 0.9396926207859084 Region R: r( 1) = -1.0000000000000000 r( 2) = 1.0000000000000000 A Gauss-Gegenbauer rule would be able to exactly integrate monomials up to and including degree = 15 Error Degree Exponents 0.0000000000000003 0 0 0.0000000000000006 1 1 0.0000000000000008 2 2 0.0000000000000005 3 3 0.0000000000000010 4 4 0.0000000000000004 5 5 0.0000000000000016 6 6 0.0000000000000004 7 7 0.0000000000000021 8 8 0.0000000000000003 9 9 0.0000000000000052 10 10 0.0000000000000003 11 11 0.0000000000000126 12 12 0.0000000000000003 13 13 0.0000000000000022 14 14 0.0000000000000002 15 15 0.0006993006993020 16 16 0.0000000000000002 17 17 0.0032908268202344 18 18 0.0000000000000002 19 19 INT_EXACTNESS_GEGENBAUER: Normal end of execution. 25 February 2008 4:56:14.102 PM