Description
1. [30 pts] Modify your code from PS12 to solve the Lorenz equations using the trapezoidal
method instead.
Generate two 10,000-point-long trajectories using h = 0.01, one from the initial condition
[x, y, z]
T = [1, 1, 1]T and the other from the initial condition [x, y, z]
T = [1.01, 1.01, 1.01]T
.
Make time-domain plots of the x coordinates and state-space plots for both trajectories.
Now explore the difference between forward Euler and trapezoidal by generating trajectories from [x, y, z]
T = [1, 1, 1]T
for a range of different time steps (e.g., h = 0.01, h =
0.001, h = 0.0001) with these two solvers and make time-domain plots of their x coordinates. In these plots, keep the overall length the same—length in time, that is, not the
number (N) of points. (Recall that h is a time interval.) You’ll probably want to zoom
in on the first second or so of the plot in order to focus this exploration.
Comment on the similarities and differences between the results produced by these two
solvers. Which are better, would you think? Why?
Please turn in your plots, your thoughts, and a copy of your code.
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