Unformatted text preview: gives the same result. I is the identity operator: ( Iu ) i = u i . 2. Show that u i = ∑ j = i j =1 h ( Du ) j . Deduce that  u  ≤  Du  , where  u  2 = ∑ i = N1 i =1 u 2 i h. 3. Show that if the function f is twice continuously diﬀerentiable, and if the equationy 00 = f,y (0) = y (1) = 0 , is approximated by (D + D) u = f,u = u N = 0 , , then the norm  yu  of the error vector with components y iu i equals C ( x ) h 2 + O ( h 4 ), where C ( x ) is independent of h . 1...
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 Fall '08
 Rieffel
 Math, Numerical Analysis, Vector Space, Englishlanguage films, Linear map, Identity function, D+

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