Solve the one-dimensional heat diffusion equation ut(x, t) = k uxx(x, t) , (0 < x < a, t > 0) subject to the following boundary conditions: ux(0, t) = 0, ux(a, t) = 0 , u(x, 0) = x (a - x), and u(x, t) bounded as t ? ?.
Added by Margaret G.
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Step 1
First, we need to find the eigenfunctions and eigenvalues of the given boundary conditions. The boundary conditions are homogeneous Neumann boundary conditions, which are given by: Ux(0,t) = 0 and Ux(a,t) = 0, where a = 4. Show more…
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