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= (a) An approximation method with a stepsize of h 0.2 produces an error of 0.05. 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 0.5 had been used instead? Give your answer rounded to at least 4 decimal places. = = (b) An approximation method which is O(h4) produces an error of 0.8 when a stepsize of h 0.7 is used. The approximation method is run again with a different stepsize and produces an error of 0.1. What stepsize do you expect was used in the second approximation? Give your final answer rounded to two decimal places.

= (a) An approximation method with a stepsize of h 0.2 produces an error of 0.05. 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 0.5 had been used instead? Give your answer rounded to at least 4 decimal places. = = (b) An approximation method which is O(h4) produces an error of 0.8 when a stepsize of h 0.7 is used. The approximation method is run again with a different stepsize and produces an error of 0.1. What stepsize do you expect was used in the second approximation? Give your final answer rounded to two decimal places.

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) An approximation method with a stepsize of h 0.2 produces an error of 0.05. 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 0.5 had been used instead? Give your answer rounded to at least 4 decimal places. = = (b) An approximation method which is O(hª) produces an error of 0.8 when a stepsize of h = 0.7 is used. The approximation method is run again with a different stepsize and produces an error of 0.1. What stepsize do you expect was used in the second approximation? Give your final answer rounded to two decimal places.
Transcribed Image Text:(a) An approximation method with a stepsize of h 0.2 produces an error of 0.05. 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 0.5 had been used instead? Give your answer rounded to at least 4 decimal places. = = (b) An approximation method which is O(hª) produces an error of 0.8 when a stepsize of h = 0.7 is used. The approximation method is run again with a different stepsize and produces an error of 0.1. What stepsize do you expect was used in the second approximation? Give your final answer rounded to two decimal places.
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