3. Find the most accurate finite difference formula and the corresponding leading error term for the following derivatives: (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
3. Find the most accurate finite difference formula and the corresponding leading error term for the following derivatives: (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
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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Question
![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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fed051053-4bf3-451a-ac87-e1db40d07cdc%2Fd1620d30-7915-40ac-aa48-e849925fbd07%2Fxmh9xl_processed.jpeg&w=3840&q=75)
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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