Unformatted text preview: the third derivative that is secondorder accurate. To do this, you will have to use four di±erent expansions for the points x i2 , x i1 , x i +1 , and x i +2 . In each case, the expansion will be around the point x i . The interval Δ x will be used in each case of i1 and i +1, and 2Δ x will be used in each case of i2 and i + 2. The four equations must then be combined in a way to eliminate the ²rst and second derivatives. Carry enough terms along in each expansion to evaluate the ²rst term that will be truncated to determine the order of the approximation. 1...
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 Fall '08
 Meiburg
 Numerical Analysis, Derivative, Taylor Series, backward difference approximations, Chapra, central difference approximations

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