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Unformatted text preview: y (0) = 1, as well as the corresponding Euler polygons for h = 0 . 2 and h = . 1. 5. (A rather hard problem) Consider the dierential equation y =y,y (0) = 1. Approximate it by the dierence equations u = 1 ,u 1 = uhu , and u i +1u i1 =2 hu i for i > 1 ( h is the mesh size). Look for exact (analytic, nonnumerical) solutions of the dierence equation of the form u i = i , and nd values of by substitution into the dierence equation. You should obtain two solutions for , say 1 , 2 . Show that for one of them, (call it 1 ), i 1 tends to ex as h tends to zero, as it should; what does i 2 do? ( 2 is the other value of ). 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 University of California, Berkeley.
 Fall '08
 Rieffel
 Polynomials, Numerical Analysis

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