How to Solve Coupled Differential Equations ODEs in Python

I walk through how to use the scipy odeint method within Python to solve coupled Ordinary Differential Equations (ODEs) and plot the results using matplotlib. Link to Python script created in this video: github.com/vastevenson/vs-cou...
Link to the Google Doc containing the problem statement: docs.google.com/document/d/1I...
Content adapted from APMonitor.com: • Simulate Coupled Diffe...

[@dotpio8246]

This was so helpful. Straightforward, straight to the point, and really easy to understand. Thank you Vincent!!

[@IKMCDANIEL]

Vincent - you have real talent. You explained a tremendous amount of technical content in just 10min. Very well done and very helpful. Thank you so much for creating this content.

[@VincentStevenson]

Thank you for your kind words, I appreciate it!

[@joaocruz9048]

Thank you, Vicent! I was with difficult on working with more than one initial conditions and this video is really helpful.

[@ammarshahzad9627]

Hello mate, I was searching R_2_score and found your channel. I saw your multi disciplinary videos and I am amazed by your content. You have mastery over alot of fields and have the gift of teaching. Subscribed instantly, hope you will gain the recognition you deserve.

[@ospectrum]

Thank you so much, I am currently working on a paper of population dynamics, and your video literally saved me a ton of time!

[@4amoats]

hey, just checking up on you

[@chasefoxen9393]

Fantastic explanation, this helped me a ton with my numerical analysis homework. Straight to the point and clear!

[@schrodingergaming7]

That's a very good solution in a small time frame! Great job!

[@rajanalexander4949]

Concise and useful; thank you!
I would just comment/say that we're assigning each _vector element_ to a _variable_ @ 3:03. The ODEs themselves are represented by the dXdt assignments.

[@pineapple5923]

Thank you so much. Better than my professor by a mile!

[@animeshsinghal3405]

Thanks a lot. You got me started with this very quickly.

[@hasatamashi]

Great video, great voice, really helpful

[@michaelhanson5336]

Very helpful. Thank you!

[@ibrahimaniakh4447]

JUST EXCELLENTLY EXPLAINED. EXCELLENT, EXCELLENT, EXCELLENT. I’m immediately subscribing bruh.

[@raulfuerte5512]

Hi Vincent. This was an amazing demo of using python's IVP solver. For a school project I was wondering if you could make a video showing how to use python to solve BVPs with a combination of Neumann and Dirichlet boundary conditions.

[@user-uu4wg6xq9l]

Thank you for this video, it was extremely well explained. It was incredibly useful to me.

[@matts2565]

This video saved my life, thanks boss!!

[@yogeshwarthakare8356]

Hi, this was so useful. Would like to see more such videos on solving kinetic model using Python

[@fannumber122]

Perfect explanation thank very much.

[@saswatipal7280]

Awesome! thank you. you saved me a big time.

[@h.a.3030]

First thank you for this simple well explained video,i'm actually working on the same model dynamics, i am wondering if you can help me for example to see the evolution of just one variable with respect to a changing parameter, i tried to use a loops, but i can't get to the results I'm expecting! TIA for any help.

[@omurwaAfrica]

This is helpful. Thank you.

[@zishanshaikh3029]

Very helpful , mate , cheers !!

[@XboxGamersAndMore]

Great vid, very helpful, thank you

[@thickeyebrows1981]

Wonderful video!

[@edholanda5897]

Professor how would I solve this system of first order edos numerically by plotting the graph for the different values ​​of (n). the derivatives are in relation to ha (r).
a'/r = -e^2*v^2*(g^2 - 1)
g' = - a*g/r
given the boundary conditions
a(0) = n a(inf)=0
g(0) = 0 g(inf)=1
o (n) varies from 1 to 8.
where (e)=0.5 and (v)=1 are constant. please give a helping hand there, I looked for and did not find any problems like this on the python website.
I'm from Brazil.

[@anandamoymukhopadhyay5158]

Vincent you have explained the code nicely within a short span of time. If the above system contains some arbitrary parameters, then please explain how to deal with it by the help of continuation method? Waiting for your reply.

[@carolina2066]

this is very nice and helpful thanks a lot :))

[@Novoselova.Polina]

thank you! really helpful

[@Onlinefizik]

Very good,Thanks

[@trumpetjonny5783]

Nice, thank you so much 🙂

[@user-ng2jh9hv1u]

Hi Vincent, thank you for such a nice video, it's extremely useful. I was wondering if you can make a video to calculate the Lyapunov exponents of coupled nonlinear ODEs.
Thank you

[@mohamedvadhelebnououmar8779]

Thanks, very helpful

[@rodrigocesarraimundo3316]

Amazing!

[@Elpidio1000]

Thank you so much dude.

[@minhtu5059]

Thank you so much!!!

[@shivathapa3934]

Hi sir. What if there was a second order derivative in the first equation (d^2A/dt^2)? What modification would be needed in the code?

[@analuciavillelaloaiza8930]

Kinda late, but you would need to do a substitution to make two first order edos instead of one of second order. Like: u=dA/dt & du/dt=d2A/dt2.

[@jowadulkader9006]

thank you sir

[@AF-ge4pe]

what if they are coupled odes but with parameters that im asked to define with runge kutta 4th order

[@ponho9715]

Thanks :D

[@mehrdadkazemi3969]

Thank you so much

[@lonemeertens7021]

Hi Vincent, thank you for this video. I have a follow up question :) What if I have (in one of the equations) a parameter (instead of a constant) that is linked to a algebraic equation that itself is also dependend on this parameter. Can some one help me? Thanks!!

[@bryanlay5215]

What if there’s an error saying list object not callable?

[@VincentStevenson]

I would double check to make sure when you create the class object, you have the () in place before calling the object after.

[@lordyabo9910]

guys I tried to copy his code word for word and run the code, but I got nothing. Can someone give me advice on what should I do. Btw im using pydroid 3

[@MsJennifervelazquez5]

thanks, you awesome

[@lunthangify]

p = odeint(odes,r0,θ0,ϕ0,x0,z0,t)
NameError: name 'r0' is not defined