LINE_FELIPPA_RULE
Quadrature Rules for a Line Segment in 1D


LINE_FELIPPA_RULE is a FORTRAN90 library which generates the points and weights of a quadrature rule over the interior of a line segment in 1D.

Licensing:

The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.

Languages:

LINE_FELIPPA_RULE is available in a C version and a C++ version and a FORTRAN90 version and a FORTRAN77 version and a MATLAB version.

Related Data and Programs:

CCN_RULE, a FORTRAN90 program which defines a nested Clenshaw Curtis quadrature rule.

CHEBYSHEV1_RULE, a FORTRAN90 program which computes and prints a Gauss-Chebyshev type 1 quadrature rule.

CHEBYSHEV2_RULE, a FORTRAN90 program which computes and prints a Gauss-Chebyshev type 2 quadrature rule.

CLENSHAW_CURTIS_RULE, a FORTRAN90 program which defines a Clenshaw Curtis quadrature rule.

LEGENDRE_RULE, a FORTRAN90 program which computes a 1D Gauss-Legendre quadrature rule.

LINE_CVT_LLOYD, a FORTRAN90 library which applies Lloyd's iteration repeatedly to a set of N points, to compute a Centroidal Voronoi Tessellation (CVT) over the interior of a line segment in 1D.

LINE_FEKETE_RULE, a FORTRAN90 library which estimates the location of N Fekete points, for polynomial interpolation or quadrature, over the interior of a line segment in 1D.

LINE_GRID, a FORTRAN90 library which computes a grid of points over the interior of a line segment in 1D.

LINE_INTEGRALS, a FORTRAN90 library which returns the exact value of the integral of any monomial over the length of the unit line in 1D.

LINE_MONTE_CARLO, a FORTRAN90 library which applies a Monte Carlo method to estimate the integral of a function over the length of the unit line in 1D;

LINE_NCC_RULE, a FORTRAN90 library which defines a Newton Cotes Closed (NCC) rule using equally spaced points over the interior of a line segment in 1D.

LINE_NCO_RULE, a FORTRAN90 library which defines a Newton Cotes Open (NCO) rule using equally spaced points over the interior of a line segment in 1D.

PATTERSON_RULE, a FORTRAN90 program which returns the points and weights of a 1D Gauss-Patterson quadrature rule of order 1, 3, 7, 15, 31, 63, 127, 255 or 511.

Reference:

  1. Carlos Felippa,
    A compendium of FEM integration formulas for symbolic work,
    Engineering Computation,
    Volume 21, Number 8, 2004, pages 867-890.

Source Code:

Examples and Tests:

List of Routines:

You can go up one level to the FORTRAN90 source codes.


Last revised on 07 September 2014.