chebyshev2_rule, a FORTRAN90 code which generates a specific Gauss-Chebyshev type 2 quadrature rule, based on user input.
The rule is written to three files for easy use as input to other codes.
The Gauss-Chevbyshev type 2 quadrature rule is used as follows:
Integral ( A <= x <= B ) f(x) sqrt ( ( x - A ) * ( B - x ) ) dxis to be approximated by
Sum ( 1 <= i <= order ) w(i) * f(x(i))
chebyshev2_rule order a b filenamewhere
The computer code and data files described and made available on this web page are distributed under the MIT license
chebyshev2_rule is available in a C++ version and a FORTRAN90 version and a MATLAB version.
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CCN_RULE, a FORTRAN90 code which defines a nested Clenshaw Curtis quadrature rule.
CHEBYSHEV_POLYNOMIAL, a FORTRAN90 code which evaluates the Chebyshev polynomial and associated functions.
CHEBYSHEV1_RULE, a FORTRAN90 code which can compute and print a Gauss-Chebyshev type 1 quadrature rule.
CLENSHAW_CURTIS_RULE, a FORTRAN90 code which defines a Clenshaw Curtis quadrature rule.
GEGENBAUER_RULE, a FORTRAN90 code which can compute and print a Gauss-Gegenbauer quadrature rule.
GEN_HERMITE_RULE, a FORTRAN90 code which can compute and print a generalized Gauss-Hermite quadrature rule.
GEN_LAGUERRE_RULE, a FORTRAN90 code which can compute and print a generalized Gauss-Laguerre quadrature rule.
HERMITE_RULE, a FORTRAN90 code which can compute and print a Gauss-Hermite quadrature rule.
JACOBI_RULE, a FORTRAN90 code which can compute and print a Gauss-Jacobi quadrature rule.
LAGUERRE_RULE, a FORTRAN90 code which can compute and print a Gauss-Laguerre quadrature rule.
LEGENDRE_RULE, a FORTRAN90 code which can compute and print a Gauss-Legendre quadrature rule.
LEGENDRE_RULE_FAST, a FORTRAN90 code which uses a fast (order N) algorithm to compute a Gauss-Legendre quadrature rule of given order.
LINE_NCC_RULE, a FORTRAN90 code which computes a Newton Cotes Closed (NCC) quadrature rule for the line, that is, for an interval of the form [A,B], using equally spaced points which include the endpoints.
LINE_NCO_RULE, a FORTRAN90 code which computes a Newton Cotes Open (NCO) quadrature rule, using equally spaced points, over the interior of a line segment in 1D.
LOGNORMAL_RULE, a FORTRAN90 code which can compute and print a quadrature rule for functions of a variable whose logarithm is normally distributed.
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.
QUADRATURE_RULES_CHEBYSHEV2, a dataset directory which contains triples of files defining standard Gauss-Chebyshev type 2 quadrature rules.
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TRUNCATED_NORMAL_RULE, a FORTRAN90 code which computes a quadrature rule for a normal distribution that has been truncated to [A,+oo), (-oo,B] or [A,B].