Problem 1. (25 pts)

Use the AE5031_HMW1_1.m code to solve the ODE df/dt = -f, f(0) = 1.

a) [5 pts] Find the exact solution.

b) [10 pts] Use the code for various timesteps 4t and calculate the error= | Exact-

Numerical/Exact as a function of the Dt at time time t = 1.

c) [10 pts] Plot the error versus the At on a logarithmic scale to confirm that the

error decreases proportionally to the 4t (1st order accuracy)