Approximate the solution to the following partial differential equation using the BackwardDifference method. u t 2u x 2 = 0, 0 < x < 2, 0 < t; u(0, t) = u(2, t) = 0, 0 < t, u(x, 0) = sin 2 x, 0 x 2. Use m = 4, T = 0.1, and N = 2, and compare your results to the actual solution u(x, t) = e(2/4)t sin(/2)x

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