Note that you can't solve "stiff" equations using Euler's method without error or more iterations (because the slope can become near vertical in places in the solution). I think Simulink uses variable RK4 by default and it brute force solves everything within a blink of an eye.
EDIT: Watched the video, he also mentions ODE45 in MATLAB uses RK4 and RK5. Curious question (semi related): have you heard of a guy named "Carl Bender"?
[ - ] Dingo 1 point 9 monthsAug 23, 2024 18:52:44 ago (+1/-0)
This one is about accuracy of numerical computations. He talks about "computing accurately" above "mathamatical proofs". I thought about him with your post and he talks about some neat stuff here. I thought you might like it.
Had a quick watch of the first three minutes of the first video.
It is very nice when you have a problem that you can solve exactly but almost no problems are exactly solvable, that is the problem and that is why it is difficult. And all the exactly solvable problems (and there are about three or four of them, that's all) um, have already been solved unfortunately and all the rest of the interesting problems that need to be solved cannot be solved exactly ...
I've also taken a peak at lecture number three where he starts off talking about other ways to make solving x^5+x=1 into a perturbation problem, so I think that lecture number one is about to turn into hard maths and its past my bed time,...
[ + ] Dingo
[ - ] Dingo 0 points 9 monthsAug 23, 2024 17:02:46 ago (+0/-0)*
Note that you can't solve "stiff" equations using Euler's method without error or more iterations (because the slope can become near vertical in places in the solution). I think Simulink uses variable RK4 by default and it brute force solves everything within a blink of an eye.
EDIT: Watched the video, he also mentions ODE45 in MATLAB uses RK4 and RK5. Curious question (semi related): have you heard of a guy named "Carl Bender"?
[ + ] happytoes
[ - ] happytoes [op] 0 points 9 monthsAug 23, 2024 18:09:32 ago (+0/-0)
Sounds very advanced.
[ + ] Dingo
[ - ] Dingo 1 point 9 monthsAug 23, 2024 18:52:44 ago (+1/-0)
https://www.youtube.com/playlist?list=PLDS6JFNmWHR3Jm93AyLRl5t-kjx3Eo33D
[ + ] happytoes
[ - ] happytoes [op] 0 points 9 monthsAug 23, 2024 21:23:12 ago (+0/-0)
I've also taken a peak at lecture number three where he starts off talking about other ways to make solving x^5+x=1 into a perturbation problem, so I think that lecture number one is about to turn into hard maths and its past my bed time,...