= Normalized local truncation error
{title2=$\mathcal T_{h,k}=\delta_{h,k}/k$}
For a time update with one-step defect $\delta_{h,k}$ after exact solution values are inserted, the normalized defect divides by the time step $k$. If $\delta_{h,k}=O(k^{p+1})$, the normalized <local truncation error> is $O(k^p)$. A spatial mesh contributes its own powers: for a diffusion update, $\mathcal T_{h,k}=O(k+h^2)$ means $\delta_{h,k}=O(k^2+kh^2)$. Under $k=O(h^2)$ these are respectively second and fourth powers of $h$. Neither normalization changes the actual <order of a numerical method>; it changes the power used to express its residual.
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