Consider the pendulum equation (w = 1 case),0 = v, v = – sin (0). There are "two" ways of implementing the forward Euler method: An+1 vn+1 = An+1 vn +1 = = = θη + Δt.vn vn - At sin (en) or if we use the most up-to-date value of the angle for the second equation, 1 θη + Δt. vn vn_ At sin (n+¹). Code each method and plot (t) and H (0 (t), v (t)) =v² - co t = [0, 10], and for an appropriate At. 1 What are your conclusions? 2 Try to show that the second approach guarantees that the discrete Hamil- tonian, Hn is bounded Vtn = n. At. cos (6), for 3 Using the second approach, write a code that "draws numerically" the phase portrait for the pendulum equation (e.g. figure 6.7.3 in the book).
Consider the pendulum equation (w = 1 case),0 = v, v = – sin (0). There are "two" ways of implementing the forward Euler method: An+1 vn+1 = An+1 vn +1 = = = θη + Δt.vn vn - At sin (en) or if we use the most up-to-date value of the angle for the second equation, 1 θη + Δt. vn vn_ At sin (n+¹). Code each method and plot (t) and H (0 (t), v (t)) =v² - co t = [0, 10], and for an appropriate At. 1 What are your conclusions? 2 Try to show that the second approach guarantees that the discrete Hamil- tonian, Hn is bounded Vtn = n. At. cos (6), for 3 Using the second approach, write a code that "draws numerically" the phase portrait for the pendulum equation (e.g. figure 6.7.3 in the book).
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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