C DG12 10
C ..................................................................DG12 20
C DG12 30
C SUBROUTINE DQG12 DG12 40
C DG12 50
C PURPOSE DG12 60
C TO COMPUTE INTEGRAL(FCT(X), SUMMED OVER X FROM XL TO XU) DG12 70
C DG12 80
C USAGE DG12 90
C CALL DQG12 (XL,XU,FCT,Y) DG12 100
C PARAMETER FCT REQUIRES AN EXTERNAL STATEMENT DG12 110
C DG12 120
C DESCRIPTION OF PARAMETERS DG12 130
C XL - DOUBLE PRECISION LOWER BOUND OF THE INTERVAL. DG12 140
C XU - DOUBLE PRECISION UPPER BOUND OF THE INTERVAL. DG12 150
C FCT - THE NAME OF AN EXTERNAL DOUBLE PRECISION FUNCTION DG12 160
C SUBPROGRAM USED. DG12 170
C Y - THE RESULTING DOUBLE PRECISION INTEGRAL VALUE. DG12 180
C DG12 190
C REMARKS DG12 200
C NONE DG12 210
C DG12 220
C SUBROUTINES AND FUNCTION SUBPROGRAMS REQUIRED DG12 230
C THE EXTERNAL DOUBLE PRECISION FUNCTION SUBPROGRAM FCT(X) DG12 240
C MUST BE FURNISHED BY THE USER. DG12 250
C DG12 260
C METHOD DG12 270
C EVALUATION IS DONE BY MEANS OF 12-POINT GAUSS QUADRATURE DG12 280
C FORMULA, WHICH INTEGRATES POLYNOMIALS UP TO DEGREE 23 DG12 290
C EXACTLY. FOR REFERENCE, SEE DG12 300
C V.I.KRYLOV, APPROXIMATE CALCULATION OF INTEGRALS, DG12 310
C MACMILLAN, NEW YORK/LONDON, 1962, PP.100-111 AND 337-340. DG12 320
C DG12 330
C ..................................................................DG12 340
C DG12 350
SUBROUTINE DQG12(XL,XU,FCT,Y) DG12 360
C DG12 370
C DG12 380
DOUBLE PRECISION XL,XU,Y,A,B,C,FCT DG12 390
C DG12 400
A=.5D0*(XU+XL) DG12 410
B=XU-XL DG12 420
C=.49078031712335963D0*B DG12 430
Y=.23587668193255914D-1*(FCT(A+C)+FCT(A-C)) DG12 440
C=.45205862818523743D0*B DG12 450
Y=Y+.53469662997659215D-1*(FCT(A+C)+FCT(A-C)) DG12 460
C=.38495133709715234D0*B DG12 470
Y=Y+.8003916427167311D-1*(FCT(A+C)+FCT(A-C)) DG12 480
C=.29365897714330872D0*B DG12 490
Y=Y+.10158371336153296D0*(FCT(A+C)+FCT(A-C)) DG12 500
C=.18391574949909010D0*B DG12 510
Y=Y+.11674626826917740D0*(FCT(A+C)+FCT(A-C)) DG12 520
C=.62616704255734458D-1*B DG12 530
Y=B*(Y+.12457352290670139D0*(FCT(A+C)+FCT(A-C))) DG12 540
RETURN DG12 550
END DG12 560