26 March 2023 6:48:13.981 PM
jacobi_exactness():
FORTRAN90 version
Investigate the polynomial exactness of a Gauss-Jacobi
quadrature rule by integrating weighted
monomials up to a given degree over the [-1,+1] interval.
JACOBI_EXACTNESS: 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 = 0.500000
Exponent of (1+x), BETA = 1.50000
Spatial dimension = 1
Number of points = 2
The quadrature rule to be tested is
a Gauss-Jacobi rule
ORDER = 2
ALPHA = 0.500000
BETA = 1.50000
Standard rule:
Integral ( -1 <= x <= +1 ) (1-x)^alpha (1+x)^beta f(x) dx
is to be approximated by
sum ( 1 <= I <= ORDER ) w(i) * f(x(i)).
Weights W:
w( 1) = 0.6369718619318372
w( 2) = 0.9338244648627008
Abscissas X:
x( 1) = -0.2742918851774317
x( 2) = 0.6076252185107651
Region R:
r( 1) = -1.000000000000000
r( 2) = 1.000000000000000
A Gauss-Jacobi rule would be able to exactly
integrate monomials up to and including degree = 3
Error Degree Exponents
0.0000000000002280 0 0
0.0000000000002282 1 1
0.0000000000002280 2 2
0.0000000000002276 3 3
0.3333333333334851 4 4
0.3777777777779197 5 5
JACOBI_EXACTNESS:
Normal end of execution.
26 March 2023 6:48:13.982 PM