QC25S(3)

SYNOPSIS
SUBROUTINE QC25S (F, A, B, BL, BR, ALFA, BETA, RI, RJ, RG, RH, + RESULT, ABSERR, RESASC, INTEGR, NEV)

NAME
qc25s - To compute I = Integral of F*W over (BL,BR), with error estimate, where the weight function W has a singular behaviour of ALGEBRAICO-LOGARITHMIC type at the points A and/or B. (BL,BR) is a part of (A,B).

LIBRARY
SLATEC (QUADPACK)

CATEGORY
H2A2A2

TYPE
SINGLE PRECISION (QC25S-S, DQC25S-D)

KEYWORDS
25-POINT CLENSHAW-CURTIS INTEGRATION, QUADPACK, QUADRATURE

AUTHOR
Piessens, Robert Applied Mathematics and Programming Division K. U. Leuven de Doncker, Elise Applied Mathematics and Programming Division K. U. Leuven

DESCRIPTION
Integration rules for integrands having ALGEBRAICO-LOGARITHMIC end point singularities Standard fortran subroutine Real version PARAMETERS F - Real Function subprogram defining the integrand F(X). The actual name for F needs to be declared E X T E R N A L in the driver program. A - Real Left end point of the original interval B - Real Right end point of the original interval, B.GT.A BL - Real Lower limit of integration, BL.GE.A BR - Real Upper limit of integration, BR.LE.B ALFA - Real PARAMETER IN THE WEIGHT FUNCTION BETA - Real Parameter in the weight function RI,RJ,RG,RH - Real Modified CHEBYSHEV moments for the application of the generalized CLENSHAW-CURTIS method (computed in subroutine DQMOMO) RESULT - Real Approximation to the integral RESULT is computed by using a generalized CLENSHAW-CURTIS method if B1 = A or BR = B. in all other cases the 15-POINT KRONROD RULE is applied, obtained by optimal addition of Abscissae to the 7-POINT GAUSS RULE. ABSERR - Real Estimate of the modulus of the absolute error, which should equal or exceed ABS(I-RESULT) RESASC - Real Approximation to the integral of ABS(F*W-I/(B-A)) INTEGR - Integer Which determines the weight function = 1 W(X) = (X-A)**ALFA*(B-X)**BETA = 2 W(X) = (X-A)**ALFA*(B-X)**BETA*LOG(X-A) = 3 W(X) = (X-A)**ALFA*(B-X)**BETA*LOG(B-X) = 4 W(X) = (X-A)**ALFA*(B-X)**BETA*LOG(X-A)* LOG(B-X) NEV - Integer Number of integrand evaluations

REFERENCES
(NONE)

ROUTINES CALLED
QCHEB, QK15W, QWGTS

REVISION HISTORY (YYMMDD)
810101 DATE WRITTEN
890531 Changed all specific intrinsics to generic. (WRB)
890531 REVISION DATE from Version 3.2
891214 Prologue converted to Version 4.0 format. (BAB)