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Numerical Analysis II, Exam End Term Spring 2017
... data x0, x1 and x˜ 0, x˜ 1. Prove by induction that |xk − x˜k| ≤ C max{|x0 − x˜ 0|, |x1 − x˜ 1 ... ∈ [ 0, T ] x( 0) = x0 ∈ R (1.1) with f ∈ C∞ subject to the Lipschitz condition |f(t, x) − f(t, y)| ≤ C|x ... data x0, x1 and x˜ 0, x˜ 1. Prove by induction that |xk − x˜k| ≤ C max{|x0 − x˜ 0|, |x1 − x˜ 1 ... ∈ [ 0, T ] x( 0) = x0 ∈ R (1.1) with f ∈ C∞ subject to the Lipschitz condition |f(t, x) − f(t, y)| ≤ C|x ...
