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Unformatted text preview: , T = 411 . . . . . . . . . . . .11 4 . We then solve the discretized equation using the iteration A u ( k +1) + h 2 u ( k ) = f where = 11 . . . NN , ij = ( x i ,y j ) . 1 (a) Show that as h 0, the rate of convergence of this iteration is essentially independent of h . Hint: use the fact that the eigenvalues of A are jk =4+2cos jh +2cos kh, j,k = 1 ,...,N, h = 1 N + 1 . (b) How does inuence convergence? 2...
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 Fall '09

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