C RTWI 10
C ..................................................................RTWI 20
C RTWI 30
C SUBROUTINE RTWI RTWI 40
C RTWI 50
C PURPOSE RTWI 60
C TO SOLVE GENERAL NONLINEAR EQUATIONS OF THE FORM X=FCT(X) RTWI 70
C BY MEANS OF WEGSTEIN-S ITERATION METHOD. RTWI 80
C RTWI 90
C USAGE RTWI 100
C CALL RTWI (X,VAL,FCT,XST,EPS,IEND,IER) RTWI 110
C PARAMETER FCT REQUIRES AN EXTERNAL STATEMENT. RTWI 120
C RTWI 130
C DESCRIPTION OF PARAMETERS RTWI 140
C X - RESULTANT ROOT OF EQUATION X=FCT(X). RTWI 150
C VAL - RESULTANT VALUE OF X-FCT(X) AT ROOT X. RTWI 160
C FCT - NAME OF THE EXTERNAL FUNCTION SUBPROGRAM USED. RTWI 170
C XST - INPUT VALUE WHICH SPECIFIES THE INITIAL GUESS OF RTWI 180
C THE ROOT X. RTWI 190
C EPS - INPUT VALUE WHICH SPECIFIES THE UPPER BOUND OF THE RTWI 200
C ERROR OF RESULT X. RTWI 210
C IEND - MAXIMUM NUMBER OF ITERATION STEPS SPECIFIED. RTWI 220
C IER - RESULTANT ERROR PARAMETER CODED AS FOLLOWS RTWI 230
C IER=0 - NO ERROR, RTWI 240
C IER=1 - NO CONVERGENCE AFTER IEND ITERATION STEPS,RTWI 250
C IER=2 - AT ANY ITERATION STEP THE DENOMINATOR OF RTWI 260
C ITERATION FORMULA WAS EQUAL TO ZERO. RTWI 270
C RTWI 280
C REMARKS RTWI 290
C THE PROCEDURE IS BYPASSED AND GIVES THE ERROR MESSAGE IER=2 RTWI 300
C IF AT ANY ITERATION STEP THE DENOMINATOR OF ITERATION RTWI 310
C FORMULA WAS EQUAL TO ZERO. THAT MEANS THAT THERE IS AT RTWI 320
C LEAST ONE POINT IN THE RANGE IN WHICH ITERATION MOVES WITH RTWI 330
C DERIVATIVE OF FCT(X) EQUAL TO 1. RTWI 340
C RTWI 350
C SUBROUTINES AND FUNCTION SUBPROGRAMS REQUIRED RTWI 360
C THE EXTERNAL FUNCTION SUBPROGRAM FCT(X) MUST BE FURNISHED RTWI 370
C BY THE USER. RTWI 380
C RTWI 390
C METHOD RTWI 400
C SOLUTION OF EQUATION X=FCT(X) IS DONE BY MEANS OF RTWI 410
C WEGSTEIN-S ITERATION METHOD, WHICH STARTS AT THE INITIAL RTWI 420
C GUESS XST OF A ROOT X. ONE ITERATION STEP REQUIRES ONE RTWI 430
C EVALUATION OF FCT(X). FOR TEST ON SATISFACTORY ACCURACY SEE RTWI 440
C FORMULAE (2) OF MATHEMATICAL DESCRIPTION. RTWI 450
C FOR REFERENCE, SEE RTWI 460
C (1) G. N. LANCE, NUMERICAL METHODS FOR HIGH SPEED COMPUTERS,RTWI 470
C ILIFFE, LONDON, 1960, PP.134-138, RTWI 480
C (2) J. WEGSTEIN, ALGORITHM 2, CACM, VOL.3, ISS.2 (1960), RTWI 490
C PP.74, RTWI 500
C (3) H.C. THACHER, ALGORITHM 15, CACM, VOL.3, ISS.8 (1960), RTWI 510
C PP.475, RTWI 520
C (4) J.G. HERRIOT, ALGORITHM 26, CACM, VOL.3, ISS.11 (1960), RTWI 530
C PP.603. RTWI 540
C RTWI 550
C ..................................................................RTWI 560
C RTWI 570
SUBROUTINE RTWI(X,VAL,FCT,XST,EPS,IEND,IER) RTWI 580
C RTWI 590
C RTWI 600
C PREPARE ITERATION RTWI 610
IER=0 RTWI 620
TOL=XST RTWI 630
X=FCT(TOL) RTWI 640
A=X-XST RTWI 650
B=-A RTWI 660
TOL=X RTWI 670
VAL=X-FCT(TOL) RTWI 680
C RTWI 690
C RTWI 700
C START ITERATION LOOP RTWI 710
DO 6 I=1,IEND RTWI 720
IF(VAL)1,7,1 RTWI 730
C RTWI 740
C EQUATION IS NOT SATISFIED BY X RTWI 750
1 B=B/VAL-1. RTWI 760
IF(B)2,8,2 RTWI 770
C RTWI 780
C ITERATION IS POSSIBLE RTWI 790
2 A=A/B RTWI 800
X=X+A RTWI 810
B=VAL RTWI 820
TOL=X RTWI 830
VAL=X-FCT(TOL) RTWI 840
C RTWI 850
C TEST ON SATISFACTORY ACCURACY RTWI 860
TOL=EPS RTWI 870
D=ABS(X) RTWI 880
IF(D-1.)4,4,3 RTWI 890
3 TOL=TOL*D RTWI 900
4 IF(ABS(A)-TOL)5,5,6 RTWI 910
5 IF(ABS(VAL)-10.*TOL)7,7,6 RTWI 920
6 CONTINUE RTWI 930
C END OF ITERATION LOOP RTWI 940
C RTWI 950
C RTWI 960
C NO CONVERGENCE AFTER IEND ITERATION STEPS. ERROR RETURN. RTWI 970
IER=1 RTWI 980
7 RETURN RTWI 990
C RTWI1000
C ERROR RETURN IN CASE OF ZERO DIVISOR RTWI1010
8 IER=2 RTWI1020
RETURN RTWI1030
END RTWI1040