Use the results of Exercise 15 to approximate the solution to u t 2u x 2 = 2, 0 < x < 1

Chapter 12, Problem 12.2.16

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Use the results of Exercise 15 to approximate the solution to u t 2u x 2 = 2, 0 < x < 1, 0 < t; u(0, t) = u(1, t) = 0, 0 < t; u(x, 0) = sin x + x(1 x), with h = 0.1 and k = 0.01. Compare your answer at t = 0.25 to the actual solution u(x, t) = e2t sin x + x(1 x).

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