Numerical Method by HornbeckChapter-3, Problem 3.17 Find a forwa.pdf

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This document provides a solution for finding a forward difference expression of order h for the sixth derivative (d^6f/dx^6) of a function f. It shows that the sixth derivative can be expressed as the sixth power of the logarithm of (1+δ) divided by h, where δ is the forward difference operator.

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$Numerical Method by Hornbeck Chapter-3, Problem 3.17 Find a forward difference expression of O(h) for d^6f/dx^6. Solution d6f/dx6 = D6 We know that - E = ehD ln E = hD D = (ln E) / h But, E = 1 + delta D = ln(1+delta) / h D6 = {ln(1+delta) / h}^6 d6f/dx6 = ln(1+delta) / h}^6 where, delta = forward difference operator$

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