Derive the following higher order finite divided difference formulas (First derivative backward difference, First derivative centered difference, Second derivative forward difference) using Taylor series expansion: 3f(x) – 4f(x1-1) + f(xi-2) f'(x,) = 2h f'(x,) ==F(xi+2) + 8f(x;+1) – 8f(x-1) +f(x¡-2) 12h
Derive the following higher order finite divided difference formulas (First derivative backward difference, First derivative centered difference, Second derivative forward difference) using Taylor series expansion: 3f(x) – 4f(x1-1) + f(xi-2) f'(x,) = 2h f'(x,) ==F(xi+2) + 8f(x;+1) – 8f(x-1) +f(x¡-2) 12h
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Derive the following higher order finite divided difference formulas (First derivative backward
difference, First derivative centered difference, Second derivative forward difference) using Taylor
series expansion:
3f(x) – 4f(x1-1) + f(xi-2)
f'(x,) =
2h
f'(x,) ==F(xi+2) + 8f(x;+1) – 8f(x-1) +f(x¡-2)
12h
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