Wikipedia and this book say the local truncation error of Euler method is $O(h^2)$. But this book and A friendly Introduction to Numerical Analysis say it's $O(h)$. Which is correct? I have a similar problem with implicit trapezoidal method.
EDIT
My numerical investigation shows that the LTE of Euler's method is $O(h^2)$. But I cannot understand why those texts say it is $O(h)$. For example for the ODE $$ y^{\prime}(x)=1+y/x,\qquad y(6-h)=Y(6-h) $$ where $Y$ is the exact solution of the ODE and $h=\frac{1}{2},\frac{1}{4},\frac{1}{8},\frac{1}{16}$ at $x=6$ by using only one step of Euler's method we have
$$ \begin{array}{c, lcr} h & \text{Approximate solution} & \text{Local truncation error} & \text{Error rato}\\ \hline 1/2 & 16.728488553430552 & 0.022068261937779 \\ 1/4 & 16.745199128855553 & 0.005357686512777 & 4.118990 \\ 1/8 & 16.749236360181335 & 0.001320455186995 & 4.057454 \\ 1/16 & 16.750229016164560 & 0.000327799203770 & 4.028244 \end{array} $$
As we see the step size is cut by a factor of $2$ and LTE decrease by a factor of $2^2$.
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