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(a) An approximation method with a stepsize of h = 0.7 produces an error of 0.4. If the approximation method used has an error which is O(h³), what would you expect the error to be if a stepsize of h = 0.2 had been used instead (give your answer rounded to 6 decimal places)? (b) An approximation method which is O(h4) produces an error of 0.8 when a stepsize of h = 0.5 is used. What stepsize should be used to obtain an error of about 0.2 instead? Give your final answer rounded to two decimal places. (c) Prove that f(x) = 7x6 — 17x¹ + 8x is NOT O(x²) as x → 0.

(a) An approximation method with a stepsize of h = 0.7 produces an error of 0.4. If the approximation method used has an error which is O(h³), what would you expect the error to be if a stepsize of h = 0.2 had been used instead (give your answer rounded to 6 decimal places)? (b) An approximation method which is O(h4) produces an error of 0.8 when a stepsize of h = 0.5 is used. What stepsize should be used to obtain an error of about 0.2 instead? Give your final answer rounded to two decimal places. (c) Prove that f(x) = 7x6 — 17x¹ + 8x is NOT O(x²) as x → 0.

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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3. (a) An approximation method with a stepsize of h = 0.7 produces an error of 0.4. If the approximation method used has an error which is O(h³), what would you expect the error to be if a stepsize of h 0.2 had been used instead (give your answer rounded to 6 = decimal places)? (b) An approximation method which is O(hª) produces an error of 0.8 when a stepsize of 0.5 is used. What stepsize should be used to obtain an error of about 0.2 instead? Give your final answer rounded to two decimal places. h = = (c) Prove that f(x) = 7x6 − 17x¹ + 8x is NOT O(x²) as x → 0.
Transcribed Image Text:3. (a) An approximation method with a stepsize of h = 0.7 produces an error of 0.4. If the approximation method used has an error which is O(h³), what would you expect the error to be if a stepsize of h 0.2 had been used instead (give your answer rounded to 6 = decimal places)? (b) An approximation method which is O(hª) produces an error of 0.8 when a stepsize of 0.5 is used. What stepsize should be used to obtain an error of about 0.2 instead? Give your final answer rounded to two decimal places. h = = (c) Prove that f(x) = 7x6 − 17x¹ + 8x is NOT O(x²) as x → 0.
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