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Unformatted text preview: diagram will suﬃce). For θ = 0 , . 5 , 1, use your code for solving: • The ODE system of Homework 2, Problem 3, with the stepsizes as indicated 1 • The predator-prey problem y 1 = . 25 y 1-. 01 y 1 y 2 y 2 =-y 2 + . 01 y 1 y 2 for 0 ≤ t ≤ 10 with stepsizes h = 0 . 1 and h = 0 . 001, and initial values y 1 = y 2 = 10. Plot y 1 vs. t and y 2 vs. t , and y 1 vs. y 2 . Note: You should write your own Newton iteration, but there is no need to write your own linear system solver. Use the func-tion provided in Matlab for that. Provide a subroutine for each problem that computes the Jacobian matrix. Do not use ﬁnite diﬀerence approximation or automatic diﬀerentiation to compute the Jacobian. DO NOT USE THE MATRIX INVERSE. IF YOU USE THE MATRIX INVERSE, YOU WILL NOT GET CREDIT FOR THIS PROBLEM! 2...
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- Spring '09
- Numerical Analysis, #, automatic differentiation, MEE 210B Homework, Solving Stiff Ordinary