Chapter 2.7, Problem 2P

(a)

To determine

The approximate values of the solution of initial value problem $y^{\prime }=2y-1,y\left(0\right)=1$ using Euler method with $h=0.1$ at $t=0.1,\text{ 0}\text{.2, 0}\text{.3, and 0}\text{.4}$.

(b)

To determine

The approximate values of the solution of initial value problem $y^{\prime }=2y-1,y\left(0\right)=1$ using Euler method with $h=0.05$ at $t=0.1,\text{ 0}\text{.2, 0}\text{.3, and 0}\text{.4}$ and compare the results with those obtained in part (a).

(c)

To determine

The approximate values of the solution of initial value problem $y^{\prime }=2y-1,y\left(0\right)=1$ using Euler method with $h=0.025$ at $t=0.1,\text{ 0}\text{.2, 0}\text{.3, and 0}\text{.4}$ and compare the results with those obtained in part (a) and part (b).

(d)

To determine

The solution $y=\varphi \left(t\right)$ and values of $\varphi \left(t\right)$ at $t=0.1,\text{ 0}\text{.2, 0}\text{.3, and 0}\text{.4}$. Also compare the results with those obtained in part (a), (b), and (c).