C QHSE 10
C ..................................................................QHSE 20
C QHSE 30
C SUBROUTINE QHSE QHSE 40
C QHSE 50
C PURPOSE QHSE 60
C TO COMPUTE THE VECTOR OF INTEGRAL VALUES FOR A GIVEN QHSE 70
C EQUIDISTANT TABLE OF FUNCTION, FIRST DERIVATIVE, QHSE 80
C AND SECOND DERIVATIVE VALUES. QHSE 90
C QHSE 100
C USAGE QHSE 110
C CALL QHSE (H,Y,FDY,SDY,Z,NDIM) QHSE 120
C QHSE 130
C DESCRIPTION OF PARAMETERS QHSE 140
C H - THE INCREMENT OF ARGUMENT VALUES. QHSE 150
C Y - THE INPUT VECTOR OF FUNCTION VALUES. QHSE 160
C FDY - THE INPUT VECTOR OF FIRST DERIVATIVE. QHSE 170
C SDY - THE INPUT VECTOR OF SECOND DERIVATIVE. QHSE 180
C Z - THE RESULTING VECTOR OF INTEGRAL VALUES. Z MAY BE QHSE 190
C IDENTICAL WITH Y,FDY OR SDY. QHSE 200
C NDIM - THE DIMENSION OF VECTORS Y,FDY,SDY,Z. QHSE 210
C QHSE 220
C REMARKS QHSE 230
C NO ACTION IN CASE NDIM LESS THAN 1. QHSE 240
C QHSE 250
C SUBROUTINES AND FUNCTION SUBPROGRAMS REQUIRED QHSE 260
C NONE QHSE 270
C QHSE 280
C METHOD QHSE 290
C BEGINNING WITH Z(1)=0, EVALUATION OF VECTOR Z IS DONE BY QHSE 300
C MEANS OF HERMITEAN SIXTH ORDER INTEGRATION FORMULA. QHSE 310
C FOR REFERENCE, SEE QHSE 320
C R.ZURMUEHL, PRAKTISCHE MATHEMATIK FUER INGENIEURE UND QHSE 330
C PHYSIKER, SPRINGER, BERLIN/GOETTINGEN/HEIDELBERG, 1963, QHSE 340
C PP.227-230. QHSE 350
C QHSE 360
C ..................................................................QHSE 370
C QHSE 380
SUBROUTINE QHSE(H,Y,FDY,SDY,Z,NDIM) QHSE 390
C QHSE 400
C QHSE 410
DIMENSION Y(1),FDY(1),SDY(1),Z(1) QHSE 420
C QHSE 430
SUM2=0. QHSE 440
IF(NDIM-1)4,3,1 QHSE 450
1 HH=.5*H QHSE 460
HF=.2*H QHSE 470
HT=.08333333*H QHSE 480
C QHSE 490
C INTEGRATION LOOP QHSE 500
DO 2 I=2,NDIM QHSE 510
SUM1=SUM2 QHSE 520
0SUM2=SUM2+HH*((Y(I-1)+Y(I))+HF*((FDY(I-1)-FDY(I))+ QHSE 530
1 HT*(SDY(I-1)+SDY(I)))) QHSE 540
2 Z(I-1)=SUM1 QHSE 550
3 Z(NDIM)=SUM2 QHSE 560
4 RETURN QHSE 570
END QHSE 580