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# CSCI3656 NUMERICAL COMPUTATION Homework 12 Solved

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## NUMERICAL COMPUTATION Homework 12

1. Read this website about the The SIR Model fo Spread of Disease – The Differential Equation
-of-disease-the-differential-equation-model

Notice the figure at the bottom of the page showing the population trajectories. You’re going to
reproduce that figure.

2. Implement Euler’s method for the SIR system. Find a stepsize h such that a plot of your Euler
trajectories matches the website’s figure. What value did you get for h, and how did you get it?

3. Repeat the previous problem with Runge-Kutta 2.

4. BONUS (20 points): Repeat the previous problem with Runge-Kutta 4.

5. BONUS (50 points): Design and run a convergence study with respect to h for both Runge-Kutta

2 and 4. Choose the range of h’s informed by (i) the values you found in problems 3 and 4 and (ii)
a goal to determine the asymptotic regime for RK2/4 applied to the SIR system. (This is such
a good problem.

This is the kind of problem you talk about in a job interview to demonstrate
your deep knowledge of the subject.)
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