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HW7 - δ = 10-6 For this problem take ± R = 10-12& ± A...

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MAT 421 Applied Computational Methods Prof. Gardner ( [email protected] ), Goldwater 654 Reading : Sections 1.1, 1.7, 4.1–4.4, 3.1–3.3, 6.1–6.4, 7.1–7.4, 7.7–7.8 of Moler’s Numerical Computing with MATLAB . Homework 7 Due: Fri Feb 24 The parameters σ = 10, r = 28, & b = 8/3 are set in LorenzEqs.m. Set t f = 40. (1) Investigate the limits of predictability for the Lorenz equations using LorenzEqs2.m by comparing the graphs of y ( t ) with initial data x (0) = 0, y (0) = 1, z (0) = 0 (red) with initial data x (0) = 0, y (0) = 1 + δ , z (0) = 0
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Unformatted text preview: δ = 10-6 . For this problem, take ± R = 10-12 & ± A = 10-15 . Discuss your results in a short paragraph. (2) Investigate convergence under re±nement of Δ t for LorenzEqs.m by com-paring the graphs of y ( t ) with ± R = 10-12 (red), ± R = 10-6 (blue), & ± R = 10-3 (green). Take ± A = 10-15 & the initial data x (0) = 0, y (0) = 1, z (0) = 0. Superimpose the three plots. Discuss your results in a short para-graph. (3) Moler Problem 7.10. Hint : Use lorenzeigs.m....
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