Chapter 8.2, Problem 15P

In each of Problems 15 and 16, estimate the local truncationerror for the Euler method in terms of the solution $y=\varphi (t)$. Obtain a bound for $e_{n+1}$ in terms of $t$ and $\varphi (t)$ that is valid on the interval $0\le t\le 1$. By using a formula for the solution, obtain a more accurate error bound for $e_{n+1}$. For $h=0.1$, compute a bound for $e_1$ and compare it with the actual error at $t=0.1$. Also compute a bound for the error $e_4$ in the fourthstep.

$\begin{array}{cc}y\text{'}=2y-1& y(0)=1\end{array}$