1 2 3 4 ! 5 ! .................................................................. 6 ! 7 ! SUBROUTINE QG2D2 8 ! 9 ! PURPOSE 10 ! TO COMPUTE INTEGRAL(FCT(X), SUMMED OVER X FROM XL TO XU) 11 ! 12 ! USAGE 13 ! CALL QG2 (XL,XU,FCT,Y) 14 ! PARAMETER FCT REQUIRES AN EXTERNAL STATEMENT 15 ! 16 ! DESCRIPTION OF PARAMETERS 17 ! XL - THE LOWER BOUND OF THE INTERVAL. 18 ! XU - THE UPPER BOUND OF THE INTERVAL. 19 ! FCT - THE NAME OF AN EXTERNAL FUNCTION SUBPROGRAM USED. 20 ! Y - THE RESULTING INTEGRAL VALUE. 21 ! 22 ! REMARKS 23 ! NONE 24 ! 25 ! SUBROUTINES AND FUNCTION SUBPROGRAMS REQUIRED 26 ! THE EXTERNAL FUNCTION SUBPROGRAM FCT(X) MUST BE FURNISHED 27 ! BY THE USER. 28 ! 29 ! METHOD 30 ! EVALUATION IS DONE BY MEANS OF 2-POINT GAUSS QUADRATURE 31 ! FORMULA, WHICH INTEGRATES POLYNOMIALS UP TO DEGREE 3 32 ! EXACTLY. 33 ! FOR REFERENCE, SEE 34 ! V.I.KRYLOV, APPROXIMATE CALCULATION OF INTEGRALS, 35 ! MACMILLAN, NEW YORK/LONDON, 1962, PP.100-111 AND 337-338. 36 ! 37 ! .................................................................. 38 ! 39 SUBROUTINE QG2D2(XL,XU,FCT,Y) 40 ! 41 ! 42 IMPLICIT NONE 43 44 REAL :: A , B , Y , XL , XU , FCT 45 EXTERNAL FCT 46 47 A = .5*(XU+XL) ! 0 48 B = XU - XL 49 Y = .2886751*B 50 Y = .5*B*(FCT(A+Y)+FCT(A-Y)) 51 52 CONTINUE 53 END
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