hmwk_1_2010

hmwk_1_2010 - UNIVERSITY OF NOTRE DAME Department of Civil...

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UNIVERSITY OF NOTRE DAME Department of Civil Engineering and Geological Sciences CE 30125 September 5, 2010 J.J. Westerink Due: September 10, 2010 Homework Set #1 Backgound: Taylor series provide a very useful and powerfull tool in order to not only derive approximations in discrete space, but also to provide valuable information about the errors that we make by using a discrete approximation. There are two key things that we want to oberve: (1) errors get larger as we apply larger discrete distances or move away from the expansion point; (2) errors have associated convergence rates - often dominated by the leading order truncated term. This information will be extremely usefull in obtaining esti- mates of how large the numerical error is for our solution and will also provide guidance as to how build our discrete “grids” or networks of nodes at which the numerical solutions are computed. Problem 1 Consider the function a) Develop 2, 4, and 6 term Taylor series expansions about x = 0.
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This note was uploaded on 03/02/2012 for the course CE 30125 taught by Professor Westerink,j during the Fall '08 term at Notre Dame.

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hmwk_1_2010 - UNIVERSITY OF NOTRE DAME Department of Civil...

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