Use the results of Exercise 15 to approximate the solution to
∂u / ∂t − ∂2u / ∂x2 = 2, 0 < x < 1, 0 < t;
u(0, t) = u(1, t) = 0, 0 < t;
u(x, 0) = sin πx + x(1 − x),
with h = 0.1 and k = 0.01. Compare your answer at t = 0.25 to the actual solution u(x, t) = e−π2t sin πx + x(1 − x).