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

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

### Languages:

LINE_NCO_RULE is available in a C version and a C++ 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_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.

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.

TETRAHEDRON_NCO_RULE, a FORTRAN90 library which defines Newton-Cotes Open (NCO) quadrature rules pver the interior of a tetrahedron in 3D.

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

### Reference:

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

### List of Routines:

• LINE_NCO_RULE computes a Newton-Cotes Open (NCO) quadrature rule.
• R8VEC_LINSPACE 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 FORTRAN90 source codes.

Last revised on 28 July 2014.