03 March 2008 08:12:31 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_o2_x.txt".
  Quadrature rule W file = "cheby2_o2_w.txt".
  Quadrature rule R file = "cheby2_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] =       0.7853981633974484
  w[ 1] =       0.7853981633974481

  Abscissas X:

  x[ 0] =      -0.4999999999999998
  x[ 1] =       0.5000000000000001

  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 = 3

          Error          Degree

                         0   0
     1.110223024625157e-16   1
     2.827159716856459e-16   2
      1.52655665885959e-16   3
        0.5000000000000003   4
      7.28583859910259e-17   5

INT_EXACTNESS_CHEBYSHEV2:
  Normal end of execution.

03 March 2008 08:12:31 AM