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hmwk_5_2010

# hmwk_5_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 November 5, 2010 J.J. Westerink Due: November 12, 2010 Homework #5 Background: Discrete differentiation applies the sums and differences of functional values to estimate the continuous derivatives to a given order of accuracy. The formulae are relative to the left most point for a forward difference approximation, to the right most point for a backward difference approximation and to the center point for a central difference approximation. We examined three ways of deriving these formulae: a) The methods of undetermined coefficients; We simply estimate the n th order accurate approximation to the p th derivative with the sum of p+n functional values ( p+n-1 functional values for central approximations to even derivatives) divided by h p . We then substitute in Taylor series approximations for the functional values, collect derivative terms and force the coefficients of these derivative terms to equal the values we want so that we end up with the derivative to the desired order.

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hmwk_5_2010 - UNIVERSITY OF NOTRE DAME Department of Civil...

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