C RTNI 10
C ..................................................................RTNI 20
C RTNI 30
C SUBROUTINE RTNI RTNI 40
C RTNI 50
C PURPOSE RTNI 60
C TO SOLVE GENERAL NONLINEAR EQUATIONS OF THE FORM F(X)=0 RTNI 70
C BY MEANS OF NEWTON-S ITERATION METHOD. RTNI 80
C RTNI 90
C USAGE RTNI 100
C CALL RTNI (X,F,DERF,FCT,XST,EPS,IEND,IER) RTNI 110
C PARAMETER FCT REQUIRES AN EXTERNAL STATEMENT. RTNI 120
C RTNI 130
C DESCRIPTION OF PARAMETERS RTNI 140
C X - RESULTANT ROOT OF EQUATION F(X)=0. RTNI 150
C F - RESULTANT FUNCTION VALUE AT ROOT X. RTNI 160
C DERF - RESULTANT VALUE OF DERIVATIVE AT ROOT X. RTNI 170
C FCT - NAME OF THE EXTERNAL SUBROUTINE USED. IT COMPUTES RTNI 180
C TO GIVEN ARGUMENT X FUNCTION VALUE F AND DERIVATIVERTNI 190
C DERF. ITS PARAMETER LIST MUST BE X,F,DERF. RTNI 200
C XST - INPUT VALUE WHICH SPECIFIES THE INITIAL GUESS OF RTNI 210
C THE ROOT X. RTNI 220
C EPS - INPUT VALUE WHICH SPECIFIES THE UPPER BOUND OF THE RTNI 230
C ERROR OF RESULT X. RTNI 240
C IEND - MAXIMUM NUMBER OF ITERATION STEPS SPECIFIED. RTNI 250
C IER - RESULTANT ERROR PARAMETER CODED AS FOLLOWS RTNI 260
C IER=0 - NO ERROR, RTNI 270
C IER=1 - NO CONVERGENCE AFTER IEND ITERATION STEPS,RTNI 280
C IER=2 - AT ANY ITERATION STEP DERIVATIVE DERF WAS RTNI 290
C EQUAL TO ZERO. RTNI 300
C RTNI 310
C REMARKS RTNI 320
C THE PROCEDURE IS BYPASSED AND GIVES THE ERROR MESSAGE IER=2 RTNI 330
C IF AT ANY ITERATION STEP DERIVATIVE OF F(X) IS EQUAL TO 0. RTNI 340
C POSSIBLY THE PROCEDURE WOULD BE SUCCESSFUL IF IT IS STARTED RTNI 350
C ONCE MORE WITH ANOTHER INITIAL GUESS XST. RTNI 360
C RTNI 370
C SUBROUTINES AND FUNCTION SUBPROGRAMS REQUIRED RTNI 380
C THE EXTERNAL SUBROUTINE FCT(X,F,DERF) MUST BE FURNISHED RTNI 390
C BY THE USER. RTNI 400
C RTNI 410
C METHOD RTNI 420
C SOLUTION OF EQUATION F(X)=0 IS DONE BY MEANS OF NEWTON-S RTNI 430
C ITERATION METHOD, WHICH STARTS AT THE INITIAL GUESS XST OF RTNI 440
C A ROOT X. CONVERGENCE IS QUADRATIC IF THE DERIVATIVE OF RTNI 450
C F(X) AT ROOT X IS NOT EQUAL TO ZERO. ONE ITERATION STEP RTNI 460
C REQUIRES ONE EVALUATION OF F(X) AND ONE EVALUATION OF THE RTNI 470
C DERIVATIVE OF F(X). FOR TEST ON SATISFACTORY ACCURACY SEE RTNI 480
C FORMULAE (2) OF MATHEMATICAL DESCRIPTION. RTNI 490
C FOR REFERENCE, SEE R. ZURMUEHL, PRAKTISCHE MATHEMATIK FUER RTNI 500
C INGENIEURE UND PHYSIKER, SPRINGER, BERLIN/GOETTINGEN/ RTNI 510
C HEIDELBERG, 1963, PP.12-17. RTNI 520
C RTNI 530
C ..................................................................RTNI 540
C RTNI 550
SUBROUTINE RTNI(X,F,DERF,FCT,XST,EPS,IEND,IER) RTNI 560
C RTNI 570
C RTNI 580
C PREPARE ITERATION RTNI 590
IER=0 RTNI 600
X=XST RTNI 610
TOL=X RTNI 620
CALL FCT(TOL,F,DERF) RTNI 630
TOLF=100.*EPS RTNI 640
C RTNI 650
C RTNI 660
C START ITERATION LOOP RTNI 670
DO 6 I=1,IEND RTNI 680
IF(F)1,7,1 RTNI 690
C RTNI 700
C EQUATION IS NOT SATISFIED BY X RTNI 710
1 IF(DERF)2,8,2 RTNI 720
C RTNI 730
C ITERATION IS POSSIBLE RTNI 740
2 DX=F/DERF RTNI 750
X=X-DX RTNI 760
TOL=X RTNI 770
CALL FCT(TOL,F,DERF) RTNI 780
C RTNI 790
C TEST ON SATISFACTORY ACCURACY RTNI 800
TOL=EPS RTNI 810
A=ABS(X) RTNI 820
IF(A-1.)4,4,3 RTNI 830
3 TOL=TOL*A RTNI 840
4 IF(ABS(DX)-TOL)5,5,6 RTNI 850
5 IF(ABS(F)-TOLF)7,7,6 RTNI 860
6 CONTINUE RTNI 870
C END OF ITERATION LOOP RTNI 880
C RTNI 890
C RTNI 900
C NO CONVERGENCE AFTER IEND ITERATION STEPS. ERROR RETURN. RTNI 910
IER=1 RTNI 920
7 RETURN RTNI 930
C RTNI 940
C ERROR RETURN IN CASE OF ZERO DIVISOR RTNI 950
8 IER=2 RTNI 960
RETURN RTNI 970
END RTNI 980