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Unformatted text preview: ( b-AT ) The value of as Ive written it depends on the lattice spacing. You can take it to be = p 2 10 . 1 a. Let T s be the steady state solution as computed in Homework 2. That is AT s = b verify that if we write T ( t ) = T s + W ( t ) then dW dt =-AW, W (0) = T (0)-T s b. Use eig to compute the eigenvalues of A for p = 10. What do you conclude about the convergence of the temperature to the steady state value? c. Suppose the sample is intially heated to a temperature of 80. Use expm to compute the temper-ature at times t = . 5 : . 5 : 5 and use surf to plot it. (Note you are solving for W so you need to add in T s to get the total temperature eld. Use p = 10.) 2...
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