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SUBROUTINE RTMI

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

USAGE
   CALL RTMI (X,F,FCT,XLI,XRI,EPS,IEND,IER)
   PARAMETER FCT REQUIRES AN EXTERNAL STATEMENT.

DESCRIPTION OF PARAMETERS
   X	  - RESULTANT ROOT OF EQUATION FCT(X)=0.
   F	  - RESULTANT FUNCTION VALUE AT ROOT X.
   FCT	  - NAME OF THE EXTERNAL FUNCTION SUBPROGRAM USED.
   XLI	  - INPUT VALUE WHICH SPECIFIES THE INITIAL LEFT BOUND
	    OF THE ROOT X.
   XRI	  - INPUT VALUE WHICH SPECIFIES THE INITIAL RIGHT BOUND
	    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
		     FOLLOWED BY IEND SUCCESSIVE STEPS OF
		     BISECTION,
	     IER=2 - BASIC ASSUMPTION FCT(XLI)*FCT(XRI) LESS
		     THAN OR EQUAL TO ZERO IS NOT SATISFIED.

REMARKS
   THE PROCEDURE ASSUMES THAT FUNCTION VALUES AT INITIAL
   BOUNDS XLI AND XRI HAVE NOT THE SAME SIGN. IF THIS BASIC
   ASSUMPTION IS NOT SATISFIED BY INPUT VALUES XLI AND XRI, THE
   PROCEDURE IS BYPASSED AND GIVES THE ERROR MESSAGE IER=2.

SUBROUTINES AND FUNCTION SUBPROGRAMS REQUIRED
   THE EXTERNAL FUNCTION SUBPROGRAM FCT(X) MUST BE FURNISHED
   BY THE USER.

METHOD
   SOLUTION OF EQUATION FCT(X)=0 IS DONE BY MEANS OF MUELLER-S
   ITERATION METHOD OF SUCCESSIVE BISECTIONS AND INVERSE
   PARABOLIC INTERPOLATION, WHICH STARTS AT THE INITIAL BOUNDS
   XLI AND XRI. CONVERGENCE IS QUADRATIC IF THE DERIVATIVE OF
   FCT(X) AT ROOT X IS NOT EQUAL TO ZERO. ONE ITERATION STEP
   REQUIRES TWO EVALUATIONS OF FCT(X). FOR TEST ON SATISFACTORY
   ACCURACY SEE FORMULAE (3,4) OF MATHEMATICAL DESCRIPTION.
   FOR REFERENCE, SEE G. K. KRISTIANSEN, ZERO OF ARBITRARY
   FUNCTION, BIT, VOL. 3 (1963), PP.205-206.