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Text File  |  1985-11-29  |  2KB  |  57 lines
  1. C
  2. C     ..................................................................
  3. C
  4. C        SUBROUTINE DQG12
  5. C
  6. C        PURPOSE
  7. C           TO COMPUTE INTEGRAL(FCT(X), SUMMED OVER X FROM XL TO XU)
  8. C
  9. C        USAGE
  10. C           CALL DQG12 (XL,XU,FCT,Y)
  11. C           PARAMETER FCT REQUIRES AN EXTERNAL STATEMENT
  12. C
  13. C        DESCRIPTION OF PARAMETERS
  14. C           XL     - DOUBLE PRECISION LOWER BOUND OF THE INTERVAL.
  15. C           XU     - DOUBLE PRECISION UPPER BOUND OF THE INTERVAL.
  16. C           FCT    - THE NAME OF AN EXTERNAL DOUBLE PRECISION FUNCTION
  17. C                    SUBPROGRAM USED.
  18. C           Y      - THE RESULTING DOUBLE PRECISION INTEGRAL VALUE.
  19. C
  20. C        REMARKS
  21. C           NONE
  22. C
  23. C        SUBROUTINES AND FUNCTION SUBPROGRAMS REQUIRED
  24. C           THE EXTERNAL DOUBLE PRECISION FUNCTION SUBPROGRAM FCT(X)
  25. C           MUST BE FURNISHED BY THE USER.
  26. C
  27. C        METHOD
  28. C           EVALUATION IS DONE BY MEANS OF 12-POINT GAUSS QUADRATURE
  29. C           FORMULA, WHICH INTEGRATES POLYNOMIALS UP TO DEGREE 23
  30. C           EXACTLY. FOR REFERENCE, SEE
  31. C           V.I.KRYLOV, APPROXIMATE CALCULATION OF INTEGRALS,
  32. C           MACMILLAN, NEW YORK/LONDON, 1962, PP.100-111 AND 337-340.
  33. C
  34. C     ..................................................................
  35. C
  36.       SUBROUTINE DQG12(XL,XU,FCT,Y)
  37. C
  38. C
  39.       DOUBLE PRECISION XL,XU,Y,A,B,C,FCT
  40. C
  41.       A=.5D0*(XU+XL)
  42.       B=XU-XL
  43.       C=.49078031712335963D0*B
  44.       Y=.23587668193255914D-1*(FCT(A+C)+FCT(A-C))
  45.       C=.45205862818523743D0*B
  46.       Y=Y+.53469662997659215D-1*(FCT(A+C)+FCT(A-C))
  47.       C=.38495133709715234D0*B
  48.       Y=Y+.8003916427167311D-1*(FCT(A+C)+FCT(A-C))
  49.       C=.29365897714330872D0*B
  50.       Y=Y+.10158371336153296D0*(FCT(A+C)+FCT(A-C))
  51.       C=.18391574949909010D0*B
  52.       Y=Y+.11674626826917740D0*(FCT(A+C)+FCT(A-C))
  53.       C=.62616704255734458D-1*B
  54.       Y=B*(Y+.12457352290670139D0*(FCT(A+C)+FCT(A-C)))
  55.       RETURN
  56.       END
  57.