03 March 2008 09:12:33 AM INT_EXACTNESS_GEGENBAUER C++ version Investigate the polynomial exactness of a Gauss-Gegenbauer quadrature rule by integrating exponentially weighted monomials up to a given degree over the (-oo,+oo) interval. INT_EXACTNESS_GEGENBAUER: User input: Quadrature rule X file = "gegen_o2_a0.5_x.txt". Quadrature rule W file = "gegen_o2_a0.5_w.txt". Quadrature rule R file = "gegen_o2_a0.5_r.txt". Maximum degree to check = 5 Exponent of (1-x^2), ALPHA = 0.5 Spatial dimension = 1 Number of points = 2 The quadrature rule to be tested is a Gauss-Gegenbauer rule ORDER = 2 ALPHA = 0.5 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[ 0] = 0.7853981633974484 w[ 1] = 0.7853981633974484 Abscissas X: x[ 0] = -0.5 x[ 1] = 0.5 Region R: r[ 0] = -1 r[ 1] = 1 A Gauss-Gegenbauer rule would be able to exactly integrate monomials up to and including degree = 3 Error Degree 7.067899292141143e-16 0 0 1 0 2 0 3 0.5000000000000001 4 0 5 INT_EXACTNESS_GEGENBAUER: Normal end of execution. 03 March 2008 09:12:33 AM