C DHSG 10
C ..................................................................DHSG 20
C DHSG 30
C SUBROUTINE DQHSG DHSG 40
C DHSG 50
C PURPOSE DHSG 60
C TO COMPUTE THE VECTOR OF INTEGRAL VALUES FOR A GIVEN DHSG 70
C GENERAL TABLE OF ARGUMENT, FUNCTION, FIRST DERIVATIVE, DHSG 80
C AND SECOND DERIVATIVE VALUES. DHSG 90
C DHSG 100
C USAGE DHSG 110
C CALL DQHSG (X,Y,FDY,SDY,Z,NDIM) DHSG 120
C DHSG 130
C DESCRIPTION OF PARAMETERS DHSG 140
C X - DOUBLE PRECISION INPUT VECTOR OF ARGUMENT VALUES. DHSG 150
C Y - DOUBLE PRECISION INPUT VECTOR OF FUNCTION VALUES. DHSG 160
C FDY - DOUBLE PRECISION INPUT VECTOR OF FIRST DERIVATIVE. DHSG 170
C SDY - DOUBLE PRECISION INPUT VECTOR OF SECOND DERIVATIVE.DHSG 180
C Z - RESULTING DOUBLE PRECISION VECTOR OF INTEGRAL DHSG 190
C VALUES. Z MAY BE IDENTICAL WITH X, Y, FDY OR SDY. DHSG 200
C NDIM - THE DIMENSION OF VECTORS X,Y,FDY,SDY,Z. DHSG 210
C DHSG 220
C REMARKS DHSG 230
C NO ACTION IN CASE NDIM LESS THAN 1. DHSG 240
C DHSG 250
C SUBROUTINES AND FUNCTION SUBPROGRAMS REQUIRED DHSG 260
C NONE DHSG 270
C DHSG 280
C METHOD DHSG 290
C BEGINNING WITH Z(1)=0, EVALUATION OF VECTOR Z IS DONE BY DHSG 300
C MEANS OF HERMITEAN SIXTH ORDER INTEGRATION FORMULA. DHSG 310
C FOR REFERENCE, SEE DHSG 320
C R.ZURMUEHL, PRAKTISCHE MATHEMATIK FUER INGENIEURE UND DHSG 330
C PHYSIKER, SPRINGER, BERLIN/GOETTINGEN/HEIDELBERG, 1963, DHSG 340
C PP.227-230. DHSG 350
C DHSG 360
C ..................................................................DHSG 370
C DHSG 380
SUBROUTINE DQHSG(X,Y,FDY,SDY,Z,NDIM) DHSG 390
C DHSG 400
C DHSG 410
DIMENSION X(1),Y(1),FDY(1),SDY(1),Z(1) DHSG 420
DOUBLE PRECISION X,Y,FDY,SDY,Z,SUM1,SUM2 DHSG 430
C DHSG 440
SUM2=0.D0 DHSG 450
IF(NDIM-1)4,3,1 DHSG 460
C DHSG 470
C INTEGRATION LOOP DHSG 480
1 DO 2 I=2,NDIM DHSG 490
SUM1=SUM2 DHSG 500
SUM2=.5D0*(X(I)-X(I-1)) DHSG 510
0SUM2=SUM1+SUM2*((Y(I-1)+Y(I))+.4D0*SUM2*((FDY(I-1)-FDY(I))+ DHSG 520
1 .16666666666666667D0*SUM2*(SDY(I-1)+SDY(I)))) DHSG 530
2 Z(I-1)=SUM1 DHSG 540
3 Z(NDIM)=SUM2 DHSG 550
4 RETURN DHSG 560
END DHSG 570