C QG9 10
C ..................................................................QG9 20
C QG9 30
C SUBROUTINE QG9 QG9 40
C QG9 50
C PURPOSE QG9 60
C TO COMPUTE INTEGRAL(FCT(X), SUMMED OVER X FROM XL TO XU) QG9 70
C QG9 80
C USAGE QG9 90
C CALL QG9 (XL,XU,FCT,Y) QG9 100
C PARAMETER FCT REQUIRES AN EXTERNAL STATEMENT QG9 110
C QG9 120
C DESCRIPTION OF PARAMETERS QG9 130
C XL - THE LOWER BOUND OF THE INTERVAL. QG9 140
C XU - THE UPPER BOUND OF THE INTERVAL. QG9 150
C FCT - THE NAME OF AN EXTERNAL FUNCTION SUBPROGRAM USED. QG9 160
C Y - THE RESULTING INTEGRAL VALUE. QG9 170
C QG9 180
C REMARKS QG9 190
C NONE QG9 200
C QG9 210
C SUBROUTINES AND FUNCTION SUBPROGRAMS REQUIRED QG9 220
C THE EXTERNAL FUNCTION SUBPROGRAM FCT(X) MUST BE FURNISHED QG9 230
C BY THE USER. QG9 240
C QG9 250
C METHOD QG9 260
C EVALUATION IS DONE BY MEANS OF 9-POINT GAUSS QUADRATURE QG9 270
C FORMULA, WHICH INTEGRATES POLYNOMIALS UP TO DEGREE 17 QG9 280
C EXACTLY. QG9 290
C FOR REFERENCE, SEE QG9 300
C V.I.KRYLOV, APPROXIMATE CALCULATION OF INTEGRALS, QG9 310
C MACMILLAN, NEW YORK/LONDON, 1962, PP.100-111 AND 337-338. QG9 320
C QG9 330
C ..................................................................QG9 340
C QG9 350
SUBROUTINE QG9(XL,XU,FCT,Y) QG9 360
C QG9 370
C QG9 380
A=.5*(XU+XL) QG9 390
B=XU-XL QG9 400
C=.4840801*B QG9 410
Y=.04063719*(FCT(A+C)+FCT(A-C)) QG9 420
C=.4180156*B QG9 430
Y=Y+.09032408*(FCT(A+C)+FCT(A-C)) QG9 440
C=.3066857*B QG9 450
Y=Y+.1303053*(FCT(A+C)+FCT(A-C)) QG9 460
C=.1621267*B QG9 470
Y=Y+.1561735*(FCT(A+C)+FCT(A-C)) QG9 480
Y=B*(Y+.1651197*FCT(A)) QG9 490
RETURN QG9 500
END QG9 510