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I'm studying the Euler Method trough the book "Numerical Analysis", but I didn't understand an example where we have to calculate the error of this method...

First of all we have a Corollary which defines the error of this method as follow:

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And here's the example:

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I don't understand why the error bound is $\frac{Mh}{2l} e^L(1 - 0)$ instead of $\frac{Mh}{2l} (e^L - 1)$, because I understood from the example that $a = 0$ and $t_i = 1$ so the $(t_i - a)$ which is in the corollary should be replaced with a $1$ and the answer should be: $\frac{Mh}{2l} (e^L - 1)$

I really don't understand where does the $e^L(1-0)$ come from...

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It is a misprint, it should be $$ e^{L(1-0)} $$ which is an upper bound for $$ \left(e^{L(1-0)}-1\right). $$

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