The common basis of the single-step methods discussed earlier is that each requires an amount to be added to  in order to get  . Formally, we define a general single-step method by:
Definition: A general single-step method for approximating the solution of a differential equation is a method which can be written in the form
where the function  is called the increment function and is determined by  . The increment function  is a function of  and  only.
Convergence for Single–step methods is defined by:
Definition: The single-step method (5.1) is convergent if  for all  as  and  with
 for any differential equation  which satisfies a Lipschitz condition.
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