Thu May 18 17:10:19 2023
chebyshev2_exactness_test:
Python version: 3.8.10
Test chebyshev2_exactness.
chebyshev2_exactness():
Investigate the polynomial exactness of a Gauss-Chebyshev1
type 2 quadrature rule by integrating all monomials up to a given
degree over the [-1,+1] interval.
chebyshev2_exactness: User input:
Quadrature rule X file = "cheby2_o4_x.txt".
Quadrature rule W file = "cheby2_o4_w.txt".
Quadrature rule R file = "cheby2_o4_r.txt".
Maximum degree to check = 10
Number of points = 4
The quadrature rule to be tested is
a Gauss-Chebyshev type 2 rule
ORDER = 4
Standard rule:
Integral ( -1 <= x <= +1 ) f(x) * ( 1 - x^2 ) dx
is to be approximated by
sum ( 1 <= I <= ORDER ) w(i) * f(x(i)).
Weights W:
[0.21707871 0.56831945 0.56831945 0.21707871]
Abscissas X:
[-0.80901699 -0.30901699 0.30901699 0.80901699]
Region R:
[-1. 1.]
A Gauss-Chebyshev type 2 rule would be able to exactly
integrate monomials up to and including
degree = 7
Error Degree
0.0000000000000001 0
0.0000000000000000 1
0.0000000000000000 2
0.0000000000000000 3
0.0000000000000003 4
0.0000000000000000 5
0.0000000000000001 6
0.0000000000000000 7
0.0714285714285713 8
0.0000000000000000 9
0.1904761904761904 10
chebyshev2_exactness_test:
Normal end of execution.
Thu May 18 17:10:19 2023