C QHFE 10
C ..................................................................QHFE 20
C QHFE 30
C SUBROUTINE QHFE QHFE 40
C QHFE 50
C PURPOSE QHFE 60
C TO COMPUTE THE VECTOR OF INTEGRAL VALUES FOR A GIVEN QHFE 70
C EQUIDISTANT TABLE OF FUNCTION AND DERIVATIVE VALUES. QHFE 80
C QHFE 90
C USAGE QHFE 100
C CALL QHFE (H,Y,DERY,Z,NDIM) QHFE 110
C QHFE 120
C DESCRIPTION OF PARAMETERS QHFE 130
C H - THE INCREMENT OF ARGUMENT VALUES. QHFE 140
C Y - THE INPUT VECTOR OF FUNCTION VALUES. QHFE 150
C DERY - THE INPUT VECTOR OF DERIVATIVE VALUES. QHFE 160
C Z - THE RESULTING VECTOR OF INTEGRAL VALUES. Z MAY BE QHFE 170
C IDENTICAL WITH Y OR DERY. QHFE 180
C NDIM - THE DIMENSION OF VECTORS Y,DERY,Z. QHFE 190
C QHFE 200
C REMARKS QHFE 210
C NO ACTION IN CASE NDIM LESS THAN 1. QHFE 220
C QHFE 230
C SUBROUTINES AND FUNCTION SUBPROGRAMS REQUIRED QHFE 240
C NONE QHFE 250
C QHFE 260
C METHOD QHFE 270
C BEGINNING WITH Z(1)=0, EVALUATION OF VECTOR Z IS DONE BY QHFE 280
C MEANS OF HERMITEAN FOURTH ORDER INTEGRATION FORMULA. QHFE 290
C FOR REFERENCE, SEE QHFE 300
C (1) F.B.HILDEBRAND, INTRODUCTION TO NUMERICAL ANALYSIS, QHFE 310
C MCGRAW-HILL, NEW YORK/TORONTO/LONDON, 1956, PP.314-319. QHFE 320
C (2) R.ZURMUEHL, PRAKTISCHE MATHEMATIK FUER INGENIEURE UND QHFE 330
C PHYSIKER, SPRINGER, BERLIN/GOETTINGEN/HEIDELBERG, 1963, QHFE 340
C PP.227-230. QHFE 350
C QHFE 360
C ..................................................................QHFE 370
C QHFE 380
SUBROUTINE QHFE(H,Y,DERY,Z,NDIM) QHFE 390
C QHFE 400
C QHFE 410
DIMENSION Y(1),DERY(1),Z(1) QHFE 420
C QHFE 430
SUM2=0. QHFE 440
IF(NDIM-1)4,3,1 QHFE 450
1 HH=.5*H QHFE 460
HS=.1666667*H QHFE 470
C QHFE 480
C INTEGRATION LOOP QHFE 490
DO 2 I=2,NDIM QHFE 500
SUM1=SUM2 QHFE 510
SUM2=SUM2+HH*((Y(I)+Y(I-1))+HS*(DERY(I-1)-DERY(I))) QHFE 520
2 Z(I-1)=SUM1 QHFE 530
3 Z(NDIM)=SUM2 QHFE 540
4 RETURN QHFE 550
END QHFE 560