Find the most accurate finite difference formula and the corresponding leadi following derivatives: (a) f"(x)

Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
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Complete tasks "i" through "iv" for parts a, b, and c. Be sure to use the specified function values.

3. Find the most accurate finite difference formula and the corresponding leading error term for the
following derivatives:
(a) ƒ"(x)
(b) f(iv) (x)
(c) f(x) - 3f'(x)
to the highest order of accuracy possible using only the following function values.
i fi-2, fi-1, fi, fi+1, and fi+2
ii fi, fi+1, fi+2, fi+3, and fi+4
iii fi-4, fi-3, fi-2, fi-1, and fi
iv fi-1, fi, fi+1, fi-1, fi, and fi+1
1
Transcribed Image Text:3. Find the most accurate finite difference formula and the corresponding leading error term for the following derivatives: (a) ƒ"(x) (b) f(iv) (x) (c) f(x) - 3f'(x) to the highest order of accuracy possible using only the following function values. i fi-2, fi-1, fi, fi+1, and fi+2 ii fi, fi+1, fi+2, fi+3, and fi+4 iii fi-4, fi-3, fi-2, fi-1, and fi iv fi-1, fi, fi+1, fi-1, fi, and fi+1 1
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