Compute approximate values in Prob. 7, using a finer grid (h = 0.1, k = 0.1), and notice the increase in accuracy.

Data from Prob. 7

If the string governed by the wave equation (1) starts from its equilibrium position with initial velocity g(x) = sin πx, what is its displacement at time t = 0.4 and x = 0.2, 0.4, 0.6, 0.8? (Use the present method with h = 0.2, k = 0.2. Use (8). Compare with the exact values obtained from (12).