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Part I (50%) This part is required to be submitted in class. Exercise 5.1.1.a Exercise 5.1.3:b,d Exercise 5.1.6 Exercise 5.1.7 Part II (50%) Population growth is described by an ODE of the form y0(t) = ry(t), where r is the growth rate. In a typical population, the…
This part is required to be submitted in class.
Population growth is described by an ODE of the form y0(t) = ry(t), where r is the growth rate. In a typical population, the growth rate is not a constant, but is density dependent. For example, as the population grows, there might be less food available, and as a result the growth rate decreases. We consider the following Logistic Equation:
8 | y0 | y | t 50; | (1) | ||
(t) = r(1 K )y; 0 | ||||||
< | ||||||
where 0 < y0 < K. Then the exact solution is given by
y0K
y(t) = y0 + (K y0)e rt :
Solve IVP (1) with y0 = 1000, r = 0:2, K = 4000 numerically using Euler’s method. Choose the step sizes
i
Requirements Print your pdf le and submit it in the discussion section. Submit to CCLE the code, for example: a MATLAB (or C++, C, etc) function euler.m that implements ALGORITHM 5.1 (p.267), and a MATLAB script main.m that solves the IVP (1) and plots the approximated solutions versus the exact one.