QK61 carries out a 61 point Gauss-Kronrod quadrature rule.
Discussion:
This routine approximates I = integral ( A <= X <= B ) F(X) dx with an error estimate, and J = integral ( A <= X <= B ) | F(X) | dx
Author:
Robert Piessens, Elise de Doncker-Kapenger, Christian Ueberhuber, David Kahaner
Reference:
Robert Piessens, Elise de Doncker-Kapenger, Christian Ueberhuber, David Kahaner, QUADPACK, a Subroutine Package for Automatic Integration, Springer Verlag, 1983
Parameters:
Input, external real F, the name of the function routine, of the form function f ( x ) real f real x which evaluates the integrand function.
Input, real A, B, the limits of integration.
Output, real RESULT, the estimated value of the integral. result is computed by applying the 61-point Kronrod rule (resk) obtained by optimal addition of abscissae to the 30-point Gauss rule (resg).
Output, real ABSERR, an estimate of | I - RESULT |.
Output, real RESABS, approximation to the integral of the absolute value of F.
Output, real RESASC, approximation to the integral | F-I/(B-A) | over [A,B].
Local Parameters:
centr - mid point of the interval
hlgth - half-length of the interval
absc - abscissa
fval* - function value
resg - result of the 30-point Gauss rule
resk - result of the 61-point Kronrod rule
reskh - approximation to the mean value of f
over (a,b), i.e. to i/(b-a)
Type | Intent | Optional | Attributes | Name | ||
---|---|---|---|---|---|---|
procedure(scalar_func) | :: | f | ||||
real | :: | a | ||||
real | :: | b | ||||
real | :: | result | ||||
real | :: | abserr | ||||
real | :: | resabs | ||||
real | :: | resasc |