Transform the following IBVP into a problem with homogeneous boundary conditions: Utt = Uxx, 0 < x < 1, t > 0 au(0,t) + bux(0,t) = fi(t) cu(1,t) + dux(1,t) = f2(t) u(x,0) = g(x) ut(x,0) = h(x), 0 < x < 1 where a, b, c, and d are constants.
Added by Paul W.
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To do this, we can introduce new variables and functions. Let's define a new function v(x, t) = u(x, t) - w(x, t), where w(x, t) is a solution to the following problem: wtt = wxx, 0 < x < 1, t > 0 aw(0,t) + bw_x(0,t) = fi(t) cw(1,t) + dw_x(1,t) = f2(t) w(x,0) = Show more…
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