Approximate the solution to the wave equation
∂2u / ∂t2 - 1/16π2 ∂2u/∂x2 = 0, 0 < x < 0.5, 0 < t;
u(0, t) = u(0.5, t) = 0, 0 < t,
u(x, 0) = 0, 0 ≤ x ≤ 0.5,
∂u / ∂t (x, 0) = sin 4πx, 0≤ x ≤ 0.5,
using the Finite-Difference Algorithm 12.4 with m = 4, N = 4 and T = 0.5. Compare your results at t = 0.5 to the actual solution u(x, t) = sin t sin 4πx.
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