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 diﬀerential equation y =y,y (0) = 1. Approximate it by the diﬀerence 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 diﬀerence equation of the form u i = ρ i , and ﬁnd values of ρ by substitution into the diﬀerence equation. You should obtain two solutions for ρ , say ρ 1 ,ρ 2 . Show that for one of them, (call it ρ 1 ), ρ i 1 tends to ex as h tends to zero, as it should; what does ρ i 2 do? ( ρ 2 is the other value of ρ ). 1...
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 Fall '08
 Rieffel
 Polynomials, Numerical Analysis, inner product, Chebysheﬀ polynomials Tn, corresponding Euler polygons

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