20 March 2020 05:29:43 PM JACOBI_EXACTNESS C++ version Compiled on Mar 20 2020 at 17:23:37. Investigate the polynomial exactness of a Gauss-Jacobi quadrature rule by integrating weighted monomials up to a given degree over the [-1,+1] interval. The quadrature file rootname is "jac_o2_a0.5_b1.5". The requested maximum monomial degree is = 5 JACOBI_EXACTNESS: User input: Quadrature rule X file = "jac_o2_a0.5_b1.5_x.txt". Quadrature rule W file = "jac_o2_a0.5_b1.5_w.txt". Quadrature rule R file = "jac_o2_a0.5_b1.5_r.txt". Maximum degree to check = 5 Exponent of (1-x), ALPHA = 0.5 Exponent of (1+x), BETA = 1.5 Spatial dimension = 1 Number of points = 2 The quadrature rule to be tested is a Gauss-Jacobi rule ORDER = 2 ALPHA = 0.5 BETA = 1.5 Standard rule: Integral ( -1 <= x <= +1 ) (1-x)^alpha (1+x)^beta f(x) dx is to be approximated by sum ( 1 <= I <= ORDER ) w(i) * f(x(i)). Weights W: w[ 0] = 0.6369718619318372 w[ 1] = 0.9338244648627008 Abscissas X: x[ 0] = -0.2742918851774317 x[ 1] = 0.6076252185107651 Region R: r[ 0] = -1 r[ 1] = 1 A Gauss-Jacobi rule would be able to exactly integrate monomials up to and including degree = 3 Error Degree 2.280104311644735e-13 0 2.281517891503163e-13 1 2.280104311644735e-13 2 2.274449992211023e-13 3 0.333333333333485 4 0.3777777777779197 5 JACOBI_EXACTNESS: Normal end of execution. 20 March 2020 05:29:43 PM