1
00:00:03,000 --> 00:00:05,000
Question 1 asks if forward Euler is a single step method
2
00:00:05,000 --> 00:00:08,000
If you remember from the lecture, this is true
3
00:00:08,000 --> 00:00:11,000
In fact, forward Euler is the most basic of all single-step methods
4
00:00:11,000 --> 00:00:15,000
It takes exactly one step, and no interpolation is done
5
00:00:15,000 --> 00:00:20,000
Question 2 asks whether forward Euler and trapezoidal are members of the family of Runge-Kutta methods
6
00:00:20,000 --> 00:00:21,000
This is true
7
00:00:21,000 --> 00:00:27,000
Forward Euler is a first order Runge-Kutta method, and trapezoidal is a second order Runge-Kutta method
8
00:00:27,000 --> 00:00:28,000
So this is true
9
00:00:28,000 --> 00:00:31,000
Question 3 asks what symplectic ODE solvers are good for
10
00:00:31,000 --> 00:00:35,000
Symplectic ODE solvers are good for systems that are conservative
11
00:00:35,000 --> 00:00:39,000
That is, systems where you want to conserve energy, or area in the more abstract case
12
00:00:39,000 --> 00:00:45,000
With these systems, failure to use a symplectic ODE solver can sometimes inject friction, essentially
13
00:00:45,000 --> 00:00:57,000
You can imagine, with a pendulum for example, in the non-dissipative case, if your ODE solver is injecting a little bit of error every step size, every time you take a step, this could effectively act as a numerical friction term
14
00:00:57,000 --> 00:01:04,000
This loss of energy fails to conserve energy, and symplectic ODE solvers are developed specifically to keep the energy in the system
15
00:01:04,000 --> 00:01:07,000
Or the area, depending on the system youre working with