Complexity Explorer Santa Few Institute

Nonlinear Dynamics: Mathematical and Computational Approaches (2024)

Lead instructor: Liz Bradley

This course is no longer in session.

6.3 Numerical dynamics and due diligence » Quiz

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Question 1

What is the result of

\frac{1}{[(1.300 + 0.0004) - (1.300 + 0.0006)]}

(a)

...using paper and pencil and infinite precision arithmetic?

(b)

...using a calculator that rounds all numbers to three places ("significant figures") to the right of the decimal point, i.e., this calculator rounds to and then stores three places after the decimal after each calculation?

Question 2

If the trajectories that your ODE solver produces with h = 0.1 do not change when you change the time step to h = 0.05, then h = 0.1 is probably a good choice.

Question 3

If the trajectories that your ODE solver produces with h = 0.1 do not change when you change the time step to h = 0.2, then h = 0.2 is probably a good choice.

Question 4

If the trajectories that your ODE solver produces change when you increase the precision of all the variables (e.g., by going from single-precision to double-precison arithmetic), then the computer's arithmetic system is introducing dynamical error into the solver results.

Question 5

The mathematical form of the system derivative affects the error of any ODE solver's solution of that system.