A Better Integrator? The Runge-Kutta Family of Integrators - Part 1 of 2 - Mathematical Foundation

[@edsonrodrigues3147]

I swear the god that I was just hearing a beautiful song, but it was just your class!

[@nighthawk2174]

Hard to express how good you explained this. Saved my grades or sure thank you!

[@gillesh333]

I never comment but this time it's worth it, thank you, great video

[@wassefah7779]

why dislike, we still have such people even here, uh those heaters... thank you sir highly appreciated work thank you so much.

[@mnks2413]

I would like to say that this is one of the best presentation I ever seen before. very clear and simple and staitforward presentation. It would be beter if you add the full derivation of the four k's slips of RK4. One more thing, please would you tell me which apps or software you are using to create your tutorial. thank you in advance and good luck.

[@emredag3768]

Thank you very much for the content. I can not describe how insightful it is. Have a lovely life :D

[@zhongxuanhou2727]

Watch a lot of your videos today, and thumbs up every video. Very straightforward and helpful!

[@razmy27]

Wonderful explanation! Thank you.

[@adeo6530]

such helpful videos, i appreciate every single one 👏 thank you

[@juniorsilva5713]

Amazing lecture!

[@umedina98]

Amazing explanation! Thanks for sharing

[@sachinjindal9283]

Thank You, Brilliantly explained. I am trying to automate this in MATLAB, this was helpful

[@AJ-et3vf]

That's nice. You can actually also read the documentation for ode45, the standard MATLAB ode solver. It has plenty of examples there including solving systems of ODEs or higher ODEs, which can guide you well and save time.

[@alialhameedi990]

Perfectly you have explained. Thanks a lot

[@dylaninho2500]

Very good video as always, what do you mean by the ‘weights’?

[@doktorphys810]

so Runge Kutta is derived from the terms in the Taylor series but what I don't understand is how we can say these K_i vectors could be equivalent to terms in the taylor expansion.

[@Freeball99]

That's what makes the RK method so smart. The math to derive it is not that difficult, but quite tedious - especially for the RK4 case. I thought that all that math would clutter this video and I'd lose people. Here is a derivation for the RK2 case, which is somewhat simpler than RK4, if you are interested. kzbin.info/www/bejne/jl7ConaZjqmVq7s

[@theizil5240]

Thanks so much for the video it was of a great help to me, can you make a video about the Cowel method ?

[@AlanTorresSorek]

Your videos are awesome! they have helped me a lot, thanks. I would like to know if you will talk about finite differences, i'm working with the quarter car model and i'm stuck with the equations. I'm making a real time numerical simulation of a suspension and your videos have been a great tool, thanks for all.

[@Freeball99]

Thanks for the feedback, it's nice to hear. Finite difference is conceptually much the same thing as this - a slight re-working of the math. Where are you stuck?

[@alxyok]

hey, what software do you use to draw on your ipad?

[@Freeball99]

Using an app called "Paper" by WeTransfer. Running on an iPad Pro 13 inch and using a Apple Pencil.

[@achrafbenammar6936]

you're life saver

[@michaeldifranco7551]

What software are you using? It looks really nice.

[@Freeball99]

App is "Paper" by WeTransfer running on a iPad 13-inch and using an Apple Pencil.

[@FabrizioSberla]

What are the software and the tools you used to write?

[@Freeball99]

The app is called "Paper" by WeTransfer. Running on an iPadPro 13 inch and using an Apple Pencil.

[@modernbabylonacademy8788]

Sir can I know what the software that u use to write

[@Freeball99]

The app is called "Paper" by WeTransfer. It is running on an iPad Pro 13 inch.

[@eustacenjeru7225]

Brilliant

[@comment8767]

Grrrrreat!

[@drover7476]

I love you sir