Topic: ODE integrations with the midpoint method
In this assignment you’ll implement the midpoint method (also known as RK2) to integrate a differential equation forward in time.
1) Create a file ode.py.
2) What is the analytic solution to the ODE
y'(t) = 0.1 * y(t)
with the boundary condition
y(0) = 1? Write the answer as a comment at the beginning of the file ode.py.
3) Implement the midpoint method in python and integrate the above ODE from t=0 to t=10. Output the value at t=10. Choose a timestep such that error is less than 10% (compare your result to the exact answer from part 2).
3) When you’re done, don’t forget to add the file ode.py to git and commit the changes.