4th-Order Runge Kutta Method for ODEs

Organized by textbook: learncheme.com/
Describes the 4th-order Runge-Kutta method for solving ordinary differential equations and gives an example. Made by faculty at the University of Colorado Boulder, Department of Chemical & Biological Engineering. Check out our Engineering Computing playlists: www.youtube.co...

[@DimaAntselevichDemonicOwl]

You managed to explain this better in 12 minutes than my professor in 3 hours.

[@Hurricane6220]

Nice job visualizing everything, it helped quite a bit. Thanks!

[@DrRAK]

Explained very well, I have a suggestion that you should have drawn concrete tangent lines with slopes K1, k2, k3, k4 and then the final tangent line with weighted average slope, it could be very easy to visualize better.

[@xenyatox9814]

I didn't really understand why you need to go back to you first point. You seem to have understood very well, so could you explain to me in few sentences ?

[@LucyRockprincess]

best explanation i've seen yet - thank you!

Best explanation of RK method I've seen until now. Thanks.

[@김지원-f9f1u]

Thank you very much!!
I major mathematics and I learn how to use matlab for solving ode.
It's very thoughtful and helpful video for people like me

[@yahirlyle5415]

I realize it's kinda randomly asking but do anyone know a good place to stream newly released series online?

[@blablabliam]

This is beautiful. Thanks for putting this together!

[@ayratkhalimov1648]

Thanks for sharing the video!
Question about weights of individual derivatives: why 2 to k2 and k3, but 1 to k1 and k4? Why not use weight 1 for all ks? (or any other weight)
Thanks!

[@AbishekMahe]

We use a time step of delta t / 2 for k2 and k3, hence the slope should be "more precise" because the time step is smaller.
That's why, they get a coefficient 2 in the average of k1 to k4, to take into account the fact that they are more accurate

[@박문정-l4k]

Thank you very much! This video is very clear and taking me straight to the point :D

[@markmisin]

Thank you for the great video!

[@OobairepointoO]

Thank you very much for this video. It helped me for writing my code in c to visualize the Rössler-Attraktor.

[@sudeuzal7]

why are there two different slope values at the same t value? I thought functions can't have two values at the same x-axis, right?

[@trivikrammohan6526]

A great and clear explanation :D. Thanks much!

[@mahdikarimi9669]

hi, thank you for useful videos. I have a system of 2nd order odes. there are some complex numbers (with imaginary part) in the equations. I wonder if Runge kutta worked or not.

[@noellou8072]

Hi there, i am doing a trajectory simulation for a free-fall lifeboat, however i tried solving the following motion equations to produce a trajectory
MX''=Fn(sin θ - uCos θ )
MZ''=Fn(cos θ + uSin θ ) - Mg
i had split it up into four 1st order ode
X' = Vx
Z' = Vz
Vx'=[fn*(sin θ - uCos θ )]/M
Vz'={[fn(cos θ + uSin θ )]/M} - g
however my runge kutta code produce something different.
i notice that at the right handside of my function i got a constant , and does not have any X or t like yours in the video.
t(1) = 0;% initial condition
Vx(1)=0;%initial accleration
X(1)=0;
Vz(1)=0;
Z(1)=0;%initial velocity
F_X = @(t,X,Vx) Vx;
F_Z = @(t,Z,Vz) Vz;
F_Vx = @(t,X,Vx)(0.866*(sin(thete)-0.5774*(cos(thete))));
F_Vz = @(t,Z,Vz)(0.866*(cos(thete)+0.5774*(sin(thete)))-9.81);
and my graph came out weird.
could the way i format my equations be the cause of my problem?
thank you

[@ShenZhao-u7n]

Really good teaching. Clear and vividly！

[@sillybilly5937]

Interesting you have x first and t last in your function notation. I have never seen it written that way.

[@behnamsay7168]

9:19 -- why x1(0.25) and not x(0.30)? Because as I understood x(t0+delta t)=x(0.2+0.1)=x(0.3)

[@dustincondon5557]

Super helpful - thanks!

[@zneah1137]

The subtitles are top-notch

[@jer3504]

Calculate function at t+ deltat/2 = 0.25 at 8:46? No idea why its 0.25 and no math was shown for that step. Super confusing.

[@LearnChemE]

Thanks for your question. t = 0.2, and deltat = 0.1, so 0.2 + (0.1)/2 = 0.25.

[@J1O2J2O1]

it's because t0 is 0.2 (initial condition) and going from there (t0+deltat/2) it's 0.25 as deltat/2 is 0.05

[@رضاجاسملفتهعويد]

thank you

[@jostromp7380]

Is this implicit or explicit?

[@aymenamer6290]

I want to solve system of 2nd order differential equations in two variables(x,y)and
with the second deriving of (x,y) with respect to z

[@norainshakirah4819]

Where do you get the true value? Is it given?

[@LearnChemE]

We used a MATLAB ODE solver to find the slope.

[@maymonaakrm8577]

Thank you so much!

[@a1ai]

I don't understand about the part of determining delta t. Is it random?

[@LearnChemE]

+F Lasmono Determining the correct time step to use is a problem for any initial value ODE method. You have to choose a time step over which your problem is slowly varying. Runge-Kutta 4th order only ensures that the error is significantly lower than the error would be for the same problem and the same time step using a 1st or 2nd order algorithm -- but the error still might be far.

[@a1ai]

+LearnChemE I see. More like trial and error then? Thank you for the explanation.

[@coldcoffeeworkshop5436]

bless you.

[@yue-ruhou6641]

My professor told me to watch your video

[@Mjaykhani]

Good one

[@奈米-ng3]

nice video

[@pendawarrior]

Thank you so much

[@ArashSheikholeslami]

thx

[@alshahriarislamziko6447]

Classy

[@DragnKillaSnipaPro]

So good

[@evanjones8049]

Using both x and t made this extremely confusing.....

[@blinded6502]

LOL what? You wanted it all to be only x?

[@nfsking2000]

Nice vid apart from pronunciation of Runge Kutta :)

[@MinhVu-fo6hd]

This method is so overrated. It is not accurate enough.