24 March 2020 02:56:23 PM

LEGENDRE_EXACTNESS
  C++ version

  Compiled on Mar 24 2020 at 14:52:43.

  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".

  The requested maximum monomial degree is = 10

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] =       0.3478548451374539
  w[ 1] =       0.6521451548625459
  w[ 2] =       0.6521451548625459
  w[ 3] =       0.3478548451374539

  Abscissas X:

  x[ 0] =      -0.8611363115940526
  x[ 1] =      -0.3399810435848563
  x[ 2] =       0.3399810435848563
  x[ 3] =       0.8611363115940526

  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)

     2.220446049250313e-16     1.110223024625157e-16   0
                         0     5.551115123125783e-17   1
                         0        0.2222222222222222   2
                         0                         0   3
                         0        0.7078189300411522   4
                         0                         0   5
                         0          1.33973479652492   6
                         0                         0   7
       0.05224489795918349         2.000914494741656   8
                         0                         0   9
         0.141807580174927         2.666790857310595  10

LEGENDRE_EXACTNESS:
  Normal end of execution.

24 March 2020 02:56:23 PM