Why the instructor said with enough damping, the system may still diverge with forward Euler method?

Pinbat

My thinking is because the Euler method still produces large error dependent on the time step as it's first-order convergent.

RichardChen9

Is it just me or is the bottom graph not all that convincing, since the timesteps seems to vary in size and the first one looks way off if it's supposed to be tangent?

ellenluo

What would the bottom graph look like physically? I'm having issues visualizing the motion.

archshift

If you'd like a more visual look at what's going on with Euler's Method and differential equation solving, check out this video by 3Blue1Brown (specifically, the latter half of the video).

GitMerlin

@RichardChen9, I think both do not make sense given the axes put in this way, cuz the closer a point is to the x-axis, the smaller the velocity is, and the closer one step can go. So if the origin of the coordinate system is in the center of the grid (for both images), then the trajectories would make sense.

Why the instructor said with enough damping, the system may still diverge with forward Euler method?

My thinking is because the Euler method still produces large error dependent on the time step as it's first-order convergent.

Is it just me or is the bottom graph not all that convincing, since the timesteps seems to vary in size and the first one looks way off if it's supposed to be tangent?

What would the bottom graph look like physically? I'm having issues visualizing the motion.

If you'd like a more visual look at what's going on with Euler's Method and differential equation solving, check out this video by 3Blue1Brown (specifically, the latter half of the video).

@RichardChen9, I think both do not make sense given the axes put in this way, cuz the closer a point is to the x-axis, the smaller the velocity is, and the closer one step can go. So if the origin of the coordinate system is in the center of the grid (for both images), then the trajectories would make sense.