02 March 2008 05:00:03 PM

INT_EXACTNESS_CHEBYSHEV1
  C++ version

  Investigate the polynomial exactness of a Gauss-Chebyshev
  type 1 quadrature rule by integrating weighted
  monomials up to a given degree over the [-1,+1] interval.

INT_EXACTNESS_CHEBYSHEV1: User input:
  Quadrature rule X file = "cheby1_o2_x.txt".
  Quadrature rule W file = "cheby1_o2_w.txt".
  Quadrature rule R file = "cheby1_o2_r.txt".
  Maximum degree to check = 5

  Spatial dimension = 1
  Number of points  = 2

  The quadrature rule to be tested is
  a Gauss-Legendre rule
  ORDER = 2

  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] =        1.570796326794897
  w[ 1] =        1.570796326794897

  Abscissas X:

  x[ 0] =      -0.7071067811865475
  x[ 1] =       0.7071067811865475

  Region R:

  r[ 0] =                       -1
  r[ 1] =                        1

  A Gauss-Chebyshev type 1 rule would be able to exactly
  integrate monomials up to and including degree = 3

          Error          Degree

     2.827159716856459e-16   0
                         0   1
                         0   2
                         0   3
        0.3333333333333334   4
                         0   5

INT_EXACTNESS_CHEBYSHEV1:
  Normal end of execution.

02 March 2008 05:00:03 PM