The last term can be treated by the Mean value theorem to get a bound
where  , which exists because of the continuity of  and  in a closed region. The treatment of the first term in (2.7) depends on our hypothesis. If we are prepared to assume that  also satisfies a Lipschitz condition in t (as will happen in practice), we can bound the first term in (2.7) by  where  is the Lipschitz constant for  as a function of  . Consequently,
and so from (2.6), we get
Thus the numerical solution converges as  .
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