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Unformatted text preview: 2 ( GH ) H + . . . + ( GH ) H n1 Every term has a factor GH , and  GH  ≤ C Δ t p +1 by consistency. Every term has a power of G (possibly G ) which is bounded by stability. Every term has a power of H which is bounded since the continuous problem is wellposed. There are n = t/ Δ t terms in Eq. ( ± ). Therefore as n → ∞ ,  G nH n  ≤ t Δ t e Kt C Δ t p +1 = O (Δ t p ) → The telescoping series ( ± ) is exactly how error accumulates in a di f erence equation. ( ± ) G nH n = n ± j =1 G nj ( GH ) H j1 H j1 propagates the exact solution to timelevel j1; ( GH ) is the local truncation error going From timelevel j1 to j ; and G nj propagates this error Forward with the diference method to timelevel n . 2...
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 Fall '11
 Staff
 Numerical Analysis, Approximation, Integrals, exact solution, local truncation error, consistent numerical approximations, Theorem of Numerical Analysis, exact growth factor

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