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(a) Develop a first-order method for approximating f" (x) which uses the data f (r – 5h), f (r – 3h), ƒ (x) and f (xr +4h). (b) Using the most accurate centered difference formula, approximate f" (1) and then state the error in the approximation, given f (r) = cos (r) +, for each he {0.1,0.01,0.001}. Use an accuracy of 6 digits throughout.

(a) Develop a first-order method for approximating f" (x) which uses the data f (r – 5h), f (r – 3h), ƒ (x) and f (xr +4h). (b) Using the most accurate centered difference formula, approximate f" (1) and then state the error in the approximation, given f (r) = cos (r) +, for each he {0.1,0.01,0.001}. Use an accuracy of 6 digits throughout.

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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(a) Develop a first-order method for approximating f" (x) which uses the data f (x – 5h), f (x – 3h), f (x) and f (r + 4h). (b) Using the most accurate centered difference formula, approximate f" (1) and then state the error in the approximation, given f (x) = cos (x) +, for each he {0.1,0.01,0.001}. Use an accuracy of 6 digits throughout.
Transcribed Image Text:(a) Develop a first-order method for approximating f" (x) which uses the data f (x – 5h), f (x – 3h), f (x) and f (r + 4h). (b) Using the most accurate centered difference formula, approximate f" (1) and then state the error in the approximation, given f (x) = cos (x) +, for each he {0.1,0.01,0.001}. Use an accuracy of 6 digits throughout.
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