Approximate the solution to the wave equation
∂2u / ∂t2 − ∂2u / ∂x2 = 0, 0 < x < 1, 0 < t;
u(0, t) = u(1, t) = 0, 0 < t,
u(x, 0) = sin 2πx, 0≤ x ≤ 1,
∂u / ∂t (x, 0) = 2π sin 2πx, 0≤ x ≤ 1,
using Algorithm 12.4 with h = 0.1 and k = 0.1. Compare your results at t = 0.3 to the actual solution u(x, t) = sin 2πx(cos 2πt + sin 2πt).