cc_d1_o2_exact.txt

25 January 2008 03:42:42 PM

INT_EXACTNESS
  C++ version

  Investigate the polynomial exactness of a
  quadrature rule by integrating all
  monomials up to a given degree over the [0,+1] interval.

  If necessary, the rule is adjusted to the [0,1] interval.

INT_EXACTNESS: User input:
  Quadrature rule X file = "cc_d1_o2_x.txt".
  Quadrature rule W file = "cc_d1_o2_w.txt".
  Quadrature rule R file = "cc_d1_o2_r.txt".
  Maximum degree to check = 5

  Spatial dimension = 1
  Number of points  = 2

  The quadrature rule to be tested:
  ORDER = 2

  Standard rule:
    Integral ( R[0] <= x <= R[1] ) f(x) dx
    is to be approximated by
    sum ( 1 <= I <= ORDER ) w(i) * f(x(i)).

  Weights W:

  w[ 0] =                        1
  w[ 1] =                        1

  Abscissas X:

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

  Region R:

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

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

          Error          Degree

                         0   0
                         0   1
        0.5000000000000001   2
                         1   3
                       1.5   4
                         2   5

INT_EXACTNESS:
  Normal end of execution.

25 January 2008 03:42:42 PM