= Variable-step global ODE error bound
{title2=$\|e_N\|\leq e^{LT}\left(\|e_0\|+C\sum_nh_n^{p+1}\right)$}
If a one-step map is Lipschitz with factor at most $1+Lh_n$ and its exact-start defect is at most $Ch_n^{p+1}$, iteration of the error recurrence gives the displayed global bound on a time interval of length $T$. Since $\sum h_n\leq T$, the defect sum is at most $T(\max h_n)^p$. Local tolerance control alone is not a global accuracy certificate: propagation, the number of steps, stiffness, roundoff and nonlinear-solve errors also enter. The <discrete Gronwall inequality> organizes this distinction.
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