Solve the 1D heat equation $u_t(x, t) = u_{xx}(x, t)$ for $0 < x < 1$, $0 \le t \le 0.1$ by using the explicit
F D scheme. The initial and boundary conditions are given as $u(x, 0) = f(x) = \sin(\pi x)$ and
$u(0, t) = u(1, t) = 0$. Choose $h = 0.2$, $k = 0.02$.