Assignment 2

This time your task is to use numerical methods to solve the following initial value problem (IVP):

\( y' = -2xy \)

where \( x \in [0,3]\) and \( y(0) = 2 \).

We provide you with the exact solution to help you debug your code.
Solution:

\(y(x)=2e^{-x^2}\)

You task is to create a file "rk4.py" that contains the following functionality:

1. Create a function that returns the right hand side of the given ODE.
2. Create a function that returns the exact solution of the given IVP.
3. Create a function that implements Runge-Kutta method of the 4th order (RK4). The function should not use global variables (i.e. use the function arguments to transfer any values to the function).
4. Use the function linspace from the numpy package to create evenly spaced intervals.
5. Use the function odeint from the package scipy.integrate to solve the given IVP.
6. Using your RK4 function solve the given IVP.
7. Using the matplotlib package create a chart with 3 subplots on it:
   • a plot that compares solutions
   • a plot that displays the error of the RK4 method
   • a plot that displays the error of the odeint method
8. Save your chart as the file my_rk4.pdf .

Submit your rk4.py script file and the generated chart my_rk4.pdf to the 'Assignment Dropbox'.

Assignment will be graded on a 10 point basis.

Due date is November 21, 2019 at 11:55pm, with 0.5 point penalty per day for late submission until the cut-off date of November 28, 2019 at 11:00am.