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The fourth derivative of a function f is calculated at N + 1 regularly spaced points using first-order accurate finite differences at the first respective last data point, and second-order accurate finite differences everywhere else. a) If truncation errors dominate, what is the observed order of the infinity norm of the derivative error when N is successively doubled? b) If round-off errors dominate, what is the observed order of the infinity norm of the derivative error when N is successively doubled?

The fourth derivative of a function f is calculated at N + 1 regularly spaced points using first-order accurate finite differences at the first respective last data point, and second-order accurate finite differences everywhere else. a) If truncation errors dominate, what is the observed order of the infinity norm of the derivative error when N is successively doubled? b) If round-off errors dominate, what is the observed order of the infinity norm of the derivative error when N is successively doubled?

Advanced Engineering Mathematics
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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The fourth derivative of a function \( f \) is calculated at \( N + 1 \) regularly spaced points using first-order accurate finite differences at the first respective last data point, and second-order accurate finite differences everywhere else. a) If truncation errors dominate, what is the observed order of the infinity norm of the derivative error when \( N \) is successively doubled? b) If round-off errors dominate, what is the observed order of the infinity norm of the derivative error when \( N \) is successively doubled?
Transcribed Image Text:The fourth derivative of a function \( f \) is calculated at \( N + 1 \) regularly spaced points using first-order accurate finite differences at the first respective last data point, and second-order accurate finite differences everywhere else. a) If truncation errors dominate, what is the observed order of the infinity norm of the derivative error when \( N \) is successively doubled? b) If round-off errors dominate, what is the observed order of the infinity norm of the derivative error when \( N \) is successively doubled?
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