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 πx, 0≤ x ≤ 1,
∂u / ∂t (x, 0) = 0, 0 ≤ x ≤ 1,
using the Finite-Difference Algorithm 12.4 with m = 4, N = 4, and T = 1.0. Compare your results at t = 1.0 to the actual solution u(x, t) = cos πt sin πx.