20 January 2020 01:01:48 PM

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

  The quadrature file rootname is "leg_o4".

LEGENDRE_EXACTNESS: User input:
  Quadrature rule X file = "leg_o4_x.txt".
  Quadrature rule W file = "leg_o4_w.txt".
  Quadrature rule R file = "leg_o4_r.txt".
  Maximum degree to check = 10

  Spatial dimension = 1
  Number of points  = 4

  The quadrature rule to be tested is
  a Gauss-Legendre rule
  ORDER = 4

  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] = 0.347855
  w[1] = 0.652145
  w[2] = 0.652145
  w[3] = 0.347855

  Abscissas X:

  x[0] = -0.861136
  x[1] = -0.339981
  x[2] = 0.339981
  x[3] = 0.861136

  Region R:

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

  A Gauss-Legendre rule would be able to exactly
  integrate monomials up to and including degree = 7

          Error                      Error           Degree
         (This rule)                (Trapezoid)

  2.2204460492503131e-16  1.1102230246251565e-16   0
  0.0000000000000000e+00  5.5511151231257827e-17   1
  0.0000000000000000e+00  2.2222222222222221e-01   2
  0.0000000000000000e+00  0.0000000000000000e+00   3
  0.0000000000000000e+00  7.0781893004115215e-01   4
  0.0000000000000000e+00  0.0000000000000000e+00   5
  0.0000000000000000e+00  1.3397347965249200e+00   6
  0.0000000000000000e+00  0.0000000000000000e+00   7
  5.2244897959183495e-02  2.0009144947416555e+00   8
  0.0000000000000000e+00  0.0000000000000000e+00   9
  1.4180758017492698e-01  2.6667908573105947e+00  10

LEGENDRE_EXACTNESS:
  Normal end of execution.

20 January 2020 01:01:48 PM