03 March 2008 08:12:47 AM INT_EXACTNESS_CHEBYSHEV2 C++ version Investigate the polynomial exactness of a Gauss-Chebyshev type 2 quadrature rule by integrating weighted monomials up to a given degree over the [-1,+1] interval. INT_EXACTNESS_CHEBYSHEV2: User input: Quadrature rule X file = "cheby2_o16_x.txt". Quadrature rule W file = "cheby2_o16_w.txt". Quadrature rule R file = "cheby2_o16_r.txt". Maximum degree to check = 35 Spatial dimension = 1 Number of points = 16 The quadrature rule to be tested is a Gauss-Legendre rule ORDER = 16 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[ 0] = 0.006239551412252139 w[ 1] = 0.02411551965623602 w[ 2] = 0.05121365616644202 w[ 3] = 0.08387420745120885 w[ 4] = 0.1176861850811667 w[ 5] = 0.1480830941187536 w[ 6] = 0.170959663563356 w[ 7] = 0.1832262859480331 w[ 8] = 0.1832262859480331 w[ 9] = 0.170959663563356 w[10] = 0.1480830941187536 w[11] = 0.1176861850811666 w[12] = 0.08387420745120885 w[13] = 0.05121365616644197 w[14] = 0.02411551965623597 w[15] = 0.006239551412252137 Abscissas X: x[ 0] = -0.9829730996839018 x[ 1] = -0.9324722294043556 x[ 2] = -0.850217135729614 x[ 3] = -0.7390089172206593 x[ 4] = -0.6026346363792563 x[ 5] = -0.4457383557765379 x[ 6] = -0.2736629900720829 x[ 7] = -0.09226835946330189 x[ 8] = 0.09226835946330203 x[ 9] = 0.273662990072083 x[10] = 0.4457383557765384 x[11] = 0.6026346363792564 x[12] = 0.7390089172206592 x[13] = 0.8502171357296141 x[14] = 0.9324722294043558 x[15] = 0.9829730996839018 Region R: r[ 0] = -1 r[ 1] = 1 A Gauss-Chebyshev type 2 rule would be able to exactly integrate monomials up to and including degree = 31 Error Degree 1.41357985842823e-16 0 9.020562075079397e-17 1 2.827159716856459e-16 2 2.255140518769849e-17 3 2.827159716856459e-16 4 2.34187669256869e-17 5 4.523455546970336e-16 6 1.214306433183765e-17 7 3.231039676407382e-16 8 6.071532165918825e-18 9 4.30805290187651e-16 10 4.336808689942018e-18 11 2.741488210285052e-16 12 6.938893903907228e-18 13 3.374139335735448e-16 14 1.474514954580286e-17 15 0 16 1.301042606982605e-17 17 2.381745413460316e-16 18 1.127570259384925e-17 19 2.757810478743524e-16 20 1.214306433183765e-17 21 4.72767510641747e-16 22 1.040834085586084e-17 23 7.125771174890099e-16 24 1.387778780781446e-17 25 5.985647786907683e-16 26 1.214306433183765e-17 27 4.433813175487173e-16 28 1.170938346284345e-17 29 4.892483503985846e-16 30 1.084202172485504e-17 31 2.828240713658907e-08 32 9.540979117872439e-18 33 2.468282765134871e-07 34 8.673617379884035e-18 35 INT_EXACTNESS_CHEBYSHEV2: Normal end of execution. 03 March 2008 08:12:47 AM