Thu May 25 11:05:20 2023
legendre_exactness_test():
Python version: 3.8.10
Test legendre_exactness().
legendre_exactness():
Investigate the polynomial exactness of a Gauss-Legendre
quadrature rule by integrating all monomials up to a given
degree over the [-1,+1] interval.
User input:
Quadrature rule X file = "leg_o004_x.txt".
Quadrature rule W file = "leg_o004_w.txt".
Quadrature rule R file = "leg_o004_r.txt".
Maximum degree to check = 10
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:
[0.34785485 0.65214515 0.65214515 0.34785485]
Abscissas X:
[-0.86113631 -0.33998104 0.33998104 0.86113631]
Region R:
[-1. 1.]
A Gauss-Legendre rule would be able to exactly
integrate monomials up to and including
degree = 7
Degree Error
0 0.0000000000000002
1 0.0000000000000000
2 0.0000000000000000
3 0.0000000000000000
4 0.0000000000000001
5 0.0000000000000000
6 0.0000000000000000
7 0.0000000000000000
8 0.0522448979591839
9 0.0000000000000000
10 0.1418075801749273
legendre_exactness_test():
Normal end of execution.
Thu May 25 11:05:20 2023