# line_ncc_rule

line_ncc_rule, a FORTRAN90 code which computes a Newton Cotes Closed (NCC) quadrature rule using equally spaced points over the interior of a line segment in 1D.

### Languages:

line_ncc_rule is available in a C version and a C++ version and a Fortran90 version and a MATLAB version and an Octave version and a Python version.

### Related Data and Programs:

ccn_rule, a FORTRAN90 code which defines a nested Clenshaw Curtis quadrature rule.

chebyshev1_rule, a FORTRAN90 code which computes and prints a Gauss-Chebyshev type 1 quadrature rule.

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

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

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

LINE_FEKETE_RULE, a FORTRAN90 code 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 code which returns the points and weights of a Felippa quadrature rule over the interior of a line segment in 1D.

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

LINE_INTEGRALS, a FORTRAN90 code 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 code 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 code 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 code 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 code 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 code which defines Newton-Cotes Closed quadrature rules on a tetrahedron.

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

WEDGE_FELIPPA_RULE, a FORTRAN90 code 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:

Last revised on 27 July 2020.