The accuracy of the explicit method depends on r(≤1/2). Illustrate this for Prob. 6, choosing r = 1/2 (and h = 0.2 as before). Do 4 steps. Compare the values for and 0.08 with the 3S-values in Prob. 6, which are 0.156, 0.254 (t = 0.04), 0.105, 0.170 (t = 0.08).

Data from Prob. 6

Solve the heat problem (1)–(3) by the explicit method with h = 0.2 and k = 0.01, 8 time steps, when f(x) = x if 0 ≤ x ≤ 1/2, f(x) = 1 - x if 1/2 ≤ x ≤ 1. Compare with the 3S-values 0.108, 0.175 for t = 0.08, x = 0.2, 0.4 obtained from the series (2 terms).