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Convergence not attained

 

The message

 

Convergence not obtained in attempting the solution of this equation.  Try changing the guess value and/or limits of variable abc

 

is displayed when EES is unable to solve a single equation having a single unknown.  Under normal circumstances, the equation is highlighted in the Equations window.  However, the equation may not be visible if the problem occurred in a library routine or in a file that was loaded with the $Include directive.  The variable that EES was trying to determine is identified in the error message.

 

This error is raised only when solving one equation with one unknown.  However, other variables appearing in the equation may have been set to incorrect or unexpected values due to an error in the problem formation.  

 

Under some circumstances, the equation is completely correct, but EES cannot find a solution because the guess value and / or limits for the variable are inappropriate.  The guess value and limits can be changed by using the Variable Info command.  Alternatively, rearranging the equation set may aid convergences as illustrated in the discussion of Inconsistent or Ill-Defined Equation Sets.

 

One effective way to solve a problem of this nature is to change the equation temporarily so that you provide a reasonable value for the variable that you are trying to determine.  For example, consider the following equation:

 

3*x^3-200*x^2-x-1=0

 

The guess value for x is 1 unless you set it to be something else.  EES will not solve this equation when the guess value for x is 1.0.  To determine a better guess for x, modify the equation by adding a variable called Error:

 

3*x^3-200*x^2-x-1=Error

 

Since you have introduced a new variable, it is necessary to specify a value for x.  The best alternative at this point is to create a Parametric table with variables Error and x.  Enter values for x to cover the range over which you expect x to reside.  Run the table.   Table results for -100 < x < 100 appear below. 

 

  error       x

-5.000E+06 -100

  -2.621E+06 -77.78

  -1.132E+06 -55.56

  -333301   -33.33

  -28796   -11.11 

-20588   11.11 

-111145   33.33

  -102937   55.56 

201567   77.78

  999899   100

 

It is clear from these results that a value of x in this range which solves the equation must be between 55.56 and 77.78 since that is the location for which Error becomes zero.   Return the equation to its original condition by replacing Error with 0.  Set the guess value of x to be 60 using the Variable Info command and try to run the problem again. Now it will quickly converge to a solution of x=66.67.