LINE_NCO_RULE
Newton Cotes Open (NCO) Quadrature Rules for the Interval

LINE_NCO_RULE is a FORTRAN77 library which computes a Newton Cotes Open (NCO) 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_NCO_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:

LINE_FEKETE_RULE, a FORTRAN77 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 FORTRAN77 library which returns the points and weights of a Felippa quadrature rule over the interior of a line segment in 1D.

LINE_GRID, a FORTRAN77 library which computes a grid of points over the interior of a line segment in 1D.

LINE_INTEGRALS, a FORTRAN77 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 FORTRAN77 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.

PYRAMID_RULE, a FORTRAN77 program which computes a quadrature rule over the interior of the unit pyramid in 3D;

WEDGE_FELIPPA_RULE, a FORTRAN77 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:

• line_nco_rule.f, the source code.
• line_nco_rule.sh, BASH commands to compile the source code.

Examples and Tests:

• line_nco_rule_prb.f, a sample calling program.
• line_nco_rule_prb.sh, BASH commands to compile and run the sample program.
• line_nco_rule_prb_output.txt, the output file.

List of Routines:

• LINE_NCO_RULE computes a Newton-Cotes Open (NCO) quadrature rule.
• R8VEC_LINSPACE2 creates a vector of linearly spaced values.
• TIMESTAMP prints the current YMDHMS date as a time stamp.

You can go up one level to the FORTRAN77 source codes.