1.The purpose of this exercise is to make a file test_ode_FE.py that makes use of the ode_FE function in the file ode_FE.py and automatically verifies the implementation of ode_FE. a) The solution computed by hand in Exercise 8.2 can be used as a reference solution. b) The test in a) can be made more general using the fact that if f is linear in u and does not depend on t, i.e., we have u
= ru, for some constant r, the Forward Euler method has a closed form solution as outlined in Sect. 8.2.1: un = U0(1+rΔt)n. Use this result to construct a test function test_ode_FE_2() that runs a number of steps in ode_FE and compares the computed solution with the listed formula for un.