Chapter 9.1, Problem 14E

(a)

To determine

The approximate value of $y\left(0.1\right)$ for the initial value problem $y^{\prime }=2y,y\left(0\right)=1$.

(b)

To determine

The bound for local truncation error in $y_1$ for the initial value problem $y^{\prime }=2y,y\left(0\right)=1$.

(c)

To determine

The comparison of the error in $y_1$ with obtained error bound in subpart (b).

(d)

To determine

The approximate value of $y\left(0.1\right)$ using two steps improved Euler’s method for the initial value problem $y^{\prime }=2y,y\left(0\right)=1$.

(e)

To determine

To verify: The global truncation error for Euler’s method $O\left(h^2\right)$ by comparing the error in parts (a) and (d).