Solve on a computer [using (6.5.2)] the wave equation 2u/t2 = 2u/x2 with u(0, t) = 0
Chapter 6, Problem 6.5.7(choose chapter or problem)
Solve on a computer [using (6.5.2)] the wave equation 2u/t2 = 2u/x2 with u(0, t) = 0, u(1, t) = 0, u(x, 0) = sin x and u/t(x, 0) = 0 with x = 1/100. For the initial condition for the first derivative u/t(x, 0) = 0, use a forward difference instead of the centered difference (3.5.4). Compare to analytic solution at x = 1/2, t = 1 by computing the error there (the difference between the analytic solution and the numerical solution). Pick t so that (a) x/t = 1.5 (b) x/t = 0.5 (c) To improve the calculation in part (a), let x = 1/200 but keep x/t = 1.5. (d) Compare the errors in parts (a) and (c).
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