= Residual bound for global ODE error
{title2=$\|e(t)\|\leq e^{L(t-t_0)}\|e(t_0)\|+\int_{t_0}^te^{L(t-s)}\|d(s)\|ds$}
For a differentiable approximation $\eta$, put $d=\eta'-f(t,\eta)$. If $f$ is <Lipschitz continuous> with constant $L$ on the relevant region, the exact solution's error satisfies the displayed bound by <Gronwall's inequality>. Thus a bound on the residual over the whole interval supplies an a posteriori <global error> estimate. A small estimated defect at a single step does not furnish this bound by itself.
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