Example 9. Divergence: Spiral  Find the solution to  .  Use the starting approximation    

Solution 9.

Since  for all   ,  then the iteration    will not converge to .  In this case,   is said to be a repelling fixed point and the iteration exhibits local divergence.  

Animation 6.  ( Fixed Point Iteration  Fixed Point Iteration ).  Internet hyperlink.

(c) John H. Mathews 2004