LINE_NCC_RULE
Newton Cotes Closed (NCC) Quadrature Rules for the Interval


LINE_NCC_RULE is a FORTRAN90 library which computes a Newton Cotes Closed (NCC) quadrature rule using equally spaced points 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_NCC_RULE is available in a C version and a C++ version and a FORTRAN77 version and a FORTRAN90 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_FEKETE_RULE, a FORTRAN90 library which approximates the location of Fekete points in an interval [A,B]. A family of sets of Fekete points, indexed by size N, represents an excellent choice for defining a polynomial interpolant.

LINE_FELIPPA_RULE, a FORTRAN90 library which returns the points and weights of a Felippa quadrature rule 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_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.

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

TETRAHEDRON_NCC_RULE, a FORTRAN90 library which defines Newton-Cotes Closed quadrature rules on a tetrahedron.

TRIANGLE_NCC_RULE, a FORTRAN90 library which defines Newton-Cotes Closed quadrature rules over the interior of a triangle in 2D.

WEDGE_FELIPPA_RULE, a FORTRAN90 library which returns quadratures rules for approximating integrals over the interior of the unit wedge in 3D.

Reference:

  1. Philip Davis, Philip Rabinowitz,
    Methods of Numerical Integration,
    Second Edition,
    Dover, 2007,
    ISBN: 0486453391,
    LC: QA299.3.D28.

Source Code:

Examples and Tests:

List of Routines:

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


Last revised on 09 April 2014.