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hw3 - the third derivative that is second-order accurate To...

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Numerical Analysis in Engineering ME 140A, Fall 2007 Homework #3 Due: Tuesday Oct 23, 8 am.( Note the due date !!!!) (Drop HW’s in the assigned box outside CAD lab) October 17, 2007 Reminder First midterm on thursday, 25th October during class time. 1. Problem 19.1 from Chapra, p. 467. Compute forward and backward di±erence approximations of O ( h ) and O ( h 2 ), and central di±erence approximations of O ( h 2 ) and O ( h 4 ) for the ²rst derivative of y = cos ( x ) at x = π/ 4 using a value of h = π/ 12. Estimate the true percent relative error ± t for each approximation. 2. Problem 19.3 from Chapra, p. 467 Use a Taylor series expansion to derive a centered ²nite-di±erence approximation to
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Unformatted text preview: the third derivative that is second-order accurate. To do this, you will have to use four di±erent expansions for the points x i-2 , x i-1 , x i +1 , and x i +2 . In each case, the expansion will be around the point x i . The interval Δ x will be used in each case of i-1 and i +1, and 2Δ x will be used in each case of i-2 and i + 2. The four equations must then be combined in a way to eliminate the ²rst and second derivatives. Carry enough terms along in each expansion to evaluate the ²rst term that will be truncated to determine the order of the approximation. 1...
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