QUADRULE - Quadrature Rules

QUADRULE returns the abscissas and weights for a variety of one dimensional quadrature rules for approximating the integral of a function. The best rule is generally Gauss-Legendre quadrature, but other rules offer special features, including the ability to handle certain weight functions, or infinite integration regions.

Files you may copy include:

• quadrule.f90, the source code;
• quadrule_prb.f90, the calling program;
• quadrule_prb.out, the sample output.

The list of routines includes:

• BASHFORTH_SET sets abscissas and weights for Adams-Bashforth quadrature.
• BDF_SET sets weights for backward differentiation ODE weights.
• BDFC_SET sets weights for backward differentiation corrector quadrature.
• BDFP_SET sets weights for backward differentiation predictor quadrature.
• BDF_SUM carries out an explicit backward difference quadrature rule for [0,1].
• CHEB_SET sets abscissas and weights for Chebyshev quadrature.
• CHEB_TO_SET sets up open Gauss-Chebyshev (first kind) quadrature.
• CHEB_TC_SET sets up closed Gauss-Chebyshev (first kind) quadrature.
• CHEB_U_SET sets abscissas and weights for Gauss-Chebyshev quadrature.
• D_SWAP switches two double precision values.
• DPI returns the value of pi as a double precision quantity.
• DVEC_REVERSE reverses the elements of a double precision vector.
• GAMMA computes the gamma function using Hastings's approximation.
• HERMITE_COM computes the abscissa and weights for Gauss-Hermite quadrature.
• HERMITE_RECUR finds the value and derivative of a Hermite polynomial.
• HERMITE_ROOT improves an approximate root of a Hermite polynomial.
• HERMITE_SET sets abscissas and weights for Hermite quadrature.
• JACOBI_COM computes the abscissa and weights for Gauss-Jacobi quadrature.
• JACOBI_RECUR finds the value and derivative of a Jacobi polynomial.
• JACOBI_ROOT improves an approximate root of a Jacobi polynomial.
• KRONROD_SET sets abscissas and weights for Gauss-Kronrod quadrature.
• LAGUERRE_COM computes the abscissa and weights for Gauss-Laguerre quadrature.
• LAGUERRE_RECUR finds the value and derivative of a Laguerre polynomial.
• LAGUERRE_ROOT improves an approximate root of a Laguerre polynomial.
• LAGUERRE_SET sets abscissas and weights for Laguerre quadrature.
• LAGUERRE_SUM carries out Laguerre quadrature over [ A, +Infinity ).
• LEGENDRE_COM computes abscissas and weights for Gauss-Legendre quadrature.
• LEGENDRE_RECUR finds the value and derivative of a Legendre polynomial.
• LEGENDRE_SET sets abscissas and weights for Gauss-Legendre quadrature.
• LEGENDRE_SET_COS sets a Gauss-Legendre rule for COS(X) * F(X) on [-PI/2,PI/2].
• LEGENDRE_SET_COS2 sets a Gauss-Legendre rule for COS(X) * F(X) on [0,PI/2].
• LEGENDRE_SET_LOG sets a Gauss-Legendre rule for - LOG(X) * F(X) on [0,1].
• LEGENDRE_SET_SQRTX_01 sets a Gauss-Legendre rule for SQRT(X) * F(X) on [0,1].
• LEGENDRE_SET_SQRTX2_01 sets a Gauss-Legendre rule for F(X) / SQRT(X) on [0,1].
• LEGENDRE_SET_X0_01 sets a Gauss-Legendre rule for F(X) on [0,1].
• LEGENDRE_SET_X1 sets a Gauss-Legendre rule for ( 1 + X ) * F(X) on [-1,1].
• LEGENDRE_SET_X1_01 sets a Gauss-Legendre rule for X * F(X) on [0,1].
• LEGENDRE_SET_X2 sets a Gauss-Legendre rule for ( 1 + X )**2 * F(X) on [-1,1].
• LEGENDRE_SET_X2_01 sets a Gauss-Legendre rule for X**2 * F(X) on [0,1].
• LOBATTO_SET sets abscissas and weights for Lobatto quadrature.
• LOG_GAMMA calculates the natural logarithm of GAMMA(X).
• MOULTON_SET sets weights for Adams-Moulton quadrature.
• NCC_COM computes the coefficients of a Newton-Cotes closed quadrature rule.
• NC_COM computes the coefficients of a Newton-Cotes quadrature rule.
• NCC_SET sets abscissas and weights for closed Newton-Cotes quadrature.
• NCO_COM computes the coefficients of a Newton-Cotes open quadrature rule.
• NCO_SET sets abscissas and weights for open Newton-Cotes quadrature.
• PI returns the value of pi as a double precision quantity.
• RADAU_SET sets abscissas and weights for Radau quadrature.
• RULE_ADJUST maps a quadrature rule from [A,B] to [C,D].
• SUMMER carries out a quadrature rule over a single interval.
• SUMMER_GK carries out Gauss-Kronrod quadrature over a single interval.
• SUM_SUB carries out a composite quadrature rule.
• SUM_SUB_GK carries out a composite Gauss-Kronrod rule.

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