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Derive an O(h4) five-point formula to approximate f (x0) that uses f (x0 − h), f (x0), f (x0 + h), f (x0 + 2h), and f (x0 + 3h). [Consider the expression Af (x0 − h) + Bf (x0 + h) + Cf (x0 + 2h) + Df (x0 + 3h). Expand in fourth Taylor polynomials, and choose A, B, C, and D appropriately.] |
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