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) Develop a first-order method for approximating f" (x) which uses the data f (r-h), f (x) and f (r+3h).

) Develop a first-order method for approximating f" (x) which uses the data f (r-h), f (x) and f (r+3h).

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 met hod for approximating f" (r) which uses the data f (r-h), f (x) and f (r +3h). (b) Use the three-point centred difference formula for the second derivative to ap- proximate f" (1), where f (r) = x", for h = 0.1, 0.01 and 0.001. Furthermore, determine the approximation error. Use an accuracy of 6 decimal digits for the final answers of the derivative values only.
Transcribed Image Text:(a) Develop a first-order met hod for approximating f" (r) which uses the data f (r-h), f (x) and f (r +3h). (b) Use the three-point centred difference formula for the second derivative to ap- proximate f" (1), where f (r) = x", for h = 0.1, 0.01 and 0.001. Furthermore, determine the approximation error. Use an accuracy of 6 decimal digits for the final answers of the derivative values only.
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