Laplace's Equation with Arbitrary Boundary Conditions in PYTHON 

i can't believe the quanity and quality of your content, truly awesome

I remembered the MIT physics course, with Prof. Walter Lewis! Your lessons using Python and the anaconda package are excellent! I´m from Brasil, Aracaju-SE.

Wow! This is quite impressive. Even more impressive is the sheer number of high quality videos in the last couple of days you have posted. Keep up the good work!

You've posted like 8 awesome videos in a week. I love them, keep it up!

Hi, Mr. P Solver, I just want to say - your Python video are the best on RU-vid in terms of quality, though a bit focused. At least for people, who already know a bit about what they are doing.

Again, these videos are the most interesting ones I have seen on computational methods. Thanks!

Commenting again, man I really have to thank you so much for your solving of an elliptic PDE here. It's a surprisingly very simple but effective method of solving this PDE. It turns out that your method of solving the PDE here, an iterative finite difference method, is actually the Gauss Seidel method for elliptic PDEs, which is guaranteed to converge because it's diagonally dominant. I thought that this may be useful to solve 2nd order boundary value problems, linear and nonlinear, and it works! After all, BVP ODEs can be thought of as elliptic PDEs too with only one independent variable. Again, thanks man! Now, I feel ready for getting into solving PDEs because of the added intuition and overwhelming effectiveness of this iterative finite difference method, which you demonstrated in this video.

Dude you've taught me so much it's insane, i'm flying through my numerical methods class

Sick rhymes and even sicker video! Really love the image -> BCs approach!

What a brilliant tutorial, well presented and methodical - the diss track in its own right is a work of art! XD This has really helped me with a project I'm working on investigating eddy current levitation - thanks man!

This is awesome! I only now got to watch these and am surprised you actually dealt with and solved PDEs, one of the few numerical methods topics that I haven't dived in yet. And also nice for using Numba here. I tried to learn Numba weeks ago, but there aren't much tutorials and examples to learn Numba so I gave up on it. Again, thanks very much.

Thanks for all this inspiration, your channel is one of my favorites! :)

Watching this tuto I just realized: there is only one Mr P Solver. Period.

Thank you!I really love your style.

thank you for all the wonderful videos.

Cool stuff. I recommend simulating a swing up of a cart pendulum system.

Awesome video, Learning a lot :) Thanks

Wow!! Great video!

Really great work! Could you do one on the Helmholtz equation i.e finding the eigenvalues and eigenvectors of the Laplacian?

Really cool video! I haven't watched the whole thing yet so this may be answered/fixed later on in the video, but does it matter that you are modifying the potential array in-place during the triple for loop?

Pardon me for a "Boomer moment." This was EXACTLY the assignment for my electrodynamics course 40 years ago! 😮 We programmed it in FORTRAN (the Python of the day) on a VAX mainframe with ASCII output for the plots. Of course, it took me about 25 hours of effort instead of 25 minutes.

Hi Luke! Thanks for the great video! I am really into this to reference my scientific computing problems. I want to know if you are going to solve the maxwell equation or maybe the landau lifshitz gilbert equation in the video or maybe solve it using the finite element method, rather than finite difference. It's going to be awesome.

Laplace's is such a beautiful equation

Amazing!

Awesome!

amazing really thank you

Awesome thanks

Dude you have zero right to diss analytical solutions that bad 😭 Great vid!

One doubt I have: could you have used a 2D convolution as you did in the 3D Laplace vid? Outstanding job, as always.

ok but why is the rap such a bop tho also can you upload the code to your git? There's only 1-7 there currently

damn thats was nice introduction song

Excellent, can we do this for surface temperature gradients of non-homogenous surfaces?

Hello, Mr. Solver. Thank you for your tutoring vid. I followed it step by step using Visual Studio Code. However, I can't create the Accordion shape image. Please could you give me more explanations about that?

Hi, how to implement no-slip condition for the square? for fluids

In the image section, what size of png file shall be produced for the coding to execute? What are the two colors shall be used to produce the image? Thanks a million

I was wondering, is there any way I can put streamlines over the potential plot ?

Great videos!, but It’s been hard to understand why you set those boundaries conditions (at least for me), can anyone explain what’s going on there? I would appreciate it

LOVE THE RAP!!!!!!!!!!!!

How do you set Efield=0 boundary condition?

please, can you solve Nernst-Planck equation in python when it is coupled with Poisson equation? :)

I tried checking the tutorial playlist but the link doesn't work..

Diss track legend

please upload the next tutorial video

In step 12, you're modifying in-place as you go. Some of the numbers you're using as the previous state have been modified and are in their final state. I think you need to have two 2D arrays, potential and potential_prime (your next state.)

Brother I couldn't find you in linkedin

hey man, the link is dead, could you please double check?

Ama be real with i solved Poisson's Equation with out even having an ideal about this sort of math , i think that algorithms are more natural way of solving

how about doing it in 3D???

i have some doubts can someone help?