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SUBROUTINE DRTNI

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

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

DESCRIPTION OF PARAMETERS
   X	  - DOUBLE PRECISION RESULTANT ROOT OF EQUATION F(X)=0.
   F	  - DOUBLE PRECISION RESULTANT FUNCTION VALUE AT
	    ROOT X.
   DERF   - DOUBLE PRECISION 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, WHERE
	    ALL PARAMETERS ARE DOUBLE PRECISION.
   XST	  - DOUBLE PRECISION INPUT VALUE WHICH SPECIFIES THE
	    INITIAL GUESS OF THE ROOT X.
   EPS	  - SINGLE PRECISION 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.