Unformatted text preview: u i +1 = u i + hf i , (ii) by the implicit Euler scheme u i +1 = u i + hf i +1 , each with h = 0 . 01. In each case you can ﬁnd the exact solution of the diﬀerence equation in the form u i = ρ i for some appropriate ρ ; plot by hand the solutions in each case for i = 1 , 2 , 3 , 4. How do you reconcile what you see what the fact that both schemes are convergent? which of the two is better (or more precisely, less horrible) in this case? what is the absolute value of the error at x = . 1 in each case? 1...
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This note was uploaded on 01/21/2012 for the course MATH 128A taught by Professor Rieffel during the Fall '08 term at Berkeley.
 Fall '08
 Rieffel
 Math, Numerical Analysis

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