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SUBROUTINE RTNI

PURPOSE
   TO SOLVE GENERAL NONLINEAR EQUATIONS OF THE FORM F(X)=0
   BY MEANS OF NEWTON-S ITERATION METHOD.

USAGE
   CALL RTNI (X,F,DERF,FCT,XST,EPS,IEND,IER)
   PARAMETER FCT REQUIRES AN EXTERNAL STATEMENT.

DESCRIPTION OF PARAMETERS
   X	  - RESULTANT ROOT OF EQUATION F(X)=0.
   F	  - RESULTANT FUNCTION VALUE AT ROOT X.
   DERF   - RESULTANT VALUE OF DERIVATIVE AT ROOT X.
   FCT	  - NAME OF THE EXTERNAL SUBROUTINE USED. IT COMPUTES
	    TO GIVEN ARGUMENT X FUNCTION VALUE F AND DERIVATIVE
	    DERF. ITS PARAMETER LIST MUST BE X,F,DERF.
   XST	  - INPUT VALUE WHICH SPECIFIES THE INITIAL GUESS OF
	    THE ROOT X.
   EPS	  - INPUT VALUE WHICH SPECIFIES THE UPPER BOUND OF THE
	    ERROR OF RESULT X.
   IEND   - MAXIMUM NUMBER OF ITERATION STEPS SPECIFIED.
   IER	  - RESULTANT ERROR PARAMETER CODED AS FOLLOWS
	     IER=0 - NO ERROR,
	     IER=1 - NO CONVERGENCE AFTER IEND ITERATION STEPS,
	     IER=2 - AT ANY ITERATION STEP DERIVATIVE DERF WAS
		     EQUAL TO ZERO.

REMARKS
   THE PROCEDURE IS BYPASSED AND GIVES THE ERROR MESSAGE IER=2
   IF AT ANY ITERATION STEP DERIVATIVE OF F(X) IS EQUAL TO 0.
   POSSIBLY THE PROCEDURE WOULD BE SUCCESSFUL IF IT IS STARTED
   ONCE MORE WITH ANOTHER INITIAL GUESS XST.

SUBROUTINES AND FUNCTION SUBPROGRAMS REQUIRED
   THE EXTERNAL SUBROUTINE FCT(X,F,DERF) MUST BE FURNISHED
   BY THE USER.

METHOD
   SOLUTION OF EQUATION F(X)=0 IS DONE BY MEANS OF NEWTON-S
   ITERATION METHOD, WHICH STARTS AT THE INITIAL GUESS XST OF
   A ROOT X. CONVERGENCE IS QUADRATIC IF THE DERIVATIVE OF
   F(X) AT ROOT X IS NOT EQUAL TO ZERO. ONE ITERATION STEP
   REQUIRES ONE EVALUATION OF F(X) AND ONE EVALUATION OF THE
   DERIVATIVE OF F(X). FOR TEST ON SATISFACTORY ACCURACY SEE
   FORMULAE (2) OF MATHEMATICAL DESCRIPTION.
   FOR REFERENCE, SEE R. ZURMUEHL, PRAKTISCHE MATHEMATIK FUER
   INGENIEURE UND PHYSIKER, SPRINGER, BERLIN/GOETTINGEN/
   HEIDELBERG, 1963, PP.12-17.