text: A practical method to estimate the order of convergence for a discretization method is pick step sizes  and  and calculate the resulting errors  and . The order of convergence is then approximated by the following formula:
  which comes from writing the truncation error, at the old and new grid spacings, as
  The error  is, more specifically, a global truncation error (GTE), in that it represents a sum of errors accumulated over all  iterations, as opposed to a local truncation error  (LTE) over just one iteration.
  Example of discretization methods
  Consider the ordinary differential equation
  with initial condition .  We can solve this equation using the Forward Euler scheme for numerical discretization:
  which generates the sequence
  In terms of , this sequence is as follows, from the Binomial theorem:
  The exact solution to this ODE is , corresponding to the following Taylor expansion in  for :
  In this case, the truncation error is
  so  converges to  with a convergence rate .
  Examples (continued)
  The sequence  with  was introduced above. This sequence converges with order 1 according to the convention for discretization methods.
  The sequence  with , which was also introduced above, converges with order q for every number q. It is said to converge exponentially using the convention for discretization methods. However, it only converges linearly (that is, with order 1) using the convention for iterative methods.
  Recurrent sequences and fixed points