Solve Prob. 8 with f(x) = x if 0 ≤ x ≤ 0.2, f(x) = 0.25(1 - x) if 0.2 < x ≤ 1, the other data being as before.

Data from Prob. 8

In a laterally insulated bar of length 1 let the initial temperature be f(x) = x if 0 ≤ x < 0.5, f(x) = 1 -x if 0.5 ≤ x ≤ 1. Let (1) and (3) hold. Apply the explicit method with h = 0.2, k = 0.01, 5 steps. Can you expect the solution to satisfy u(x, t) = u(1 - x, t) for all t?