(Solved): (a) Derive the first and second center difference approximations. (b) Consider the boundary value p ...

(a) Derive the first and second center difference approximations. (b) Consider the boundary value problem (BVP): 4 points $\{\begin{array}{l}{u}^{??}?t{u}^{?}+3u=e^t.0<t<1\\ u(0)=1,u(1)=2\end{array}$ Using the first and second center difference approximations with step size $h=0.2$, show that the BVP can be formulated into a linear system $AU=F$. Solve this system for the numerical solution $U$.