We define $$ \begin{equation} y'(t_i)=f(t_i,y_i) \tag{16} \end{equation} $$ and if we truncate \( \Delta \) at the first derivative, we have $$ \begin{equation} y_{i+1}=y(t_i) + hf(t_i,y_i) + O(h^2), \tag{17} \end{equation} $$ which when complemented with \( t_{i+1}=t_i+h \) forms the algorithm for the well-known Euler method. Note that at every step we make an approximation error of the order of \( O(h^2) \), however the total error is the sum over all steps \( N=(b-a)/h \), yielding thus a global error which goes like \( NO(h^2)\approx O(h) \).