QUADRATURE_RULES_LEGENDRE is a dataset directory which contains examples of quadrature rules of Gauss-Legendre type.
Gauss-Legendre quadrature rules are designed to approximate integrals on the interval [-1,1].
Standard Gauss-Legendre quadrature assumes that the integrand we are considering has a form like:
Integral ( -1 <= x <= +1 ) f(x) dx
A standard Gauss-Legendre quadrature rule is a set of n positive weights w and abscissas x so that
Integral ( -1 <= x <= +1 ) f(x) dxmay be approximated by
Sum ( 1 <= I <= N ) w(i) * f(x(i))
For this directory, a quadrature rule is stored as three files, containing the weights, the points, and a file containing two points defining the endpoints of the region.
We consider a standard Gauss-Legendre quadrature rule of order 4.
Here is the text of the "W" file storing the weights of such a rule:
0.3478548451374538
0.6521451548625461
0.6521451548625461
0.3478548451374538
Here is the text of the "X" file storing the abscissas of such a rule:
-0.8611363115940526
-0.3399810435848563
0.3399810435848563
0.8611363115940526
Here is the text of the "R" file storing the lower and upper limits of the region:
-1.0
1.0
The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.
INT_EXACTNESS_LEGENDRE, a FORTRAN90 program which can read a set of files defining a Gauss-Legendre quadrature rule, and test it for exactness against monomial integrands.
LEGENDRE_RULE, a FORTRAN90 program which generates a Gauss-Legendre rule of the desired order.
QUADRATURE_TEST, a MATLAB program which reads the definition of a multidimensional quadrature rule from three files, applies the rule to a number of test integrals, and prints the results.
QUADRULE, a FORTRAN90 library which defines various quadrature rules.
TEST_INT, a FORTRAN90 library which defines several test integrands which may be integrated.
Gauss-Legendre Rule, Order 1:
Gauss-Legendre Rule, Order 2:
Gauss-Legendre Rule, Order 3:
Gauss-Legendre Rule, Order 4:
Gauss-Legendre Rule, Order 7:
Gauss-Legendre Rule, Order 8:
Gauss-Legendre Rule, Order 15:
Gauss-Legendre Rule, Order 16:
Gauss-Legendre Rule, Order 31:
Gauss-Legendre Rule, Order 32:
Gauss-Legendre Rule, Order 63:
Gauss-Legendre Rule, Order 64:
Gauss-Legendre Rule, Order 65:
Gauss-Legendre Rule, Order 127:
You can go up one level to the DATASETS page.