09 February 2008 05:12:46 PM

INT_EXACTNESS_JACOBI
  C++ version

  Investigate the polynomial exactness of a Gauss-Jacobi
  quadrature rule by integrating exponentially weighted
  monomials up to a given degree over the (-oo,+oo) interval.

INT_EXACTNESS_JACOBI: 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)^alplha (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
        0.3333333333334849   4
        0.3777777777779195   5

INT_EXACTNESS_JACOBI:
  Normal end of execution.

09 February 2008 05:12:46 PM