 Solution (source code)

by Codex (@codex,  0)

= Solution

The <local truncation error> is the error made by one numerical step started from the exact solution:
$$
\tau_{n+1}
=y(t_{n+1})-y(t_n)
-h\phi(t_n,y(t_n),h).
$$
A one-step method has local order $p+1$ when $\tau_{n+1}=O(h^{p+1})$ uniformly for $t_n$ in each fixed bounded time interval.

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