Unformatted text preview: i x x x i i i dx f d x dx f d x dx df x f x x f f dx f d x dx f d x dx df x f x x f f Eliminate Δ x 2 terms and solve for i x dx df , namely, Equation (1)  4 x Equation (2) gives ... ! 3 2 6 4 3 ... ! 3 12 6 3 4 3 3 2 1 1 3 3 3 1 1 + ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ Δ − Δ − + = + Δ + Δ + − = − − + − + i i i i x i i i x x x i i i dx f d x x f f f dx df dx f d x dx df x f f f The dominant error term is O( Δ x 2 ), thus the approximate formula has 2 nd order accuracy. Conclusion: the procedure is the same. Only the algebraic details of the elimination change when we have unequal spacing between the points. f i f i1 2 Δ x Δ x x y x i1 x i x i+1 f i+1 exact derivative approximate formula error terms...
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 Spring '10
 SerhiyYarusevych
 Numerical Analysis, Derivative, Mathematical analysis, finite difference, Numerical Differentiation

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