Solving The 1D & 2D Heat Equation Numerically in Python || FDM Simulation - Python Tutorial #4

In this video, you will learn how to solve the 1D & 2D Heat Equation with the finite difference method using Python.



Enjoy ~ 🐍

Outline of the video :
0:00 - Introduction
1:10 - Solving the 1D Heat Equation
4:51 - Visualizing the solution
6:29 - Solving the 2D Heat Equation
10:27 - Surprise ?

[nonato]

Incrível, mano! Recentemente fiz um trabalho sobre a equação de calor e seu vídeo me deu uma nova perspectiva do que eu havia feito. Parabéns!

[vikonja]

As straightforward as this solution is, I believe it needs to be mentioned: this approach is extremely inefficient. It has time complexity O(N^2), which renders the method practically useless when applied to models/systems with a large number of cells (which ultimately is what one will have when doing serious work). A much more efficient code can be made by adjusting to use scipy's sparse module and solvers for sparce matrices.
A good video nonetheless, if you want to get a preview of how the finite-difference method works ;) just mentioning a relevant computational aspect

[saamirjassim]

Stability of solution also accuracy comparing with another solutions .. Thanks alot .

[vdl]

Awesome tutorial! I recommend you use libraries like manim for 3d visualizations as well!

[omaramdyaze]

keep going bro , we need more solving physics problem using python, I hope if you have a vid about heat diffusion resolution for rectangular section fins and temperature profiles and thanks in advance bro

[feweir]

where do you take all formulas, for example that for get dd_ux and dd_uy ^

[EdwardHe-jrvg]

Hi! It's very awesome video and very straight forward! A quick question, do you know if there's any chance to speed up the process with cuda?

[oskarmakala]

Could anyone explain why is it necessary to use a copy of array u in the scheme equation? I know that it gives slightly different results if we just rewrite u array in each loop, thanks

[madlynlv]

Thank you for this tutorial. Please show me how to plot 3D graph of Riemann Zeta function where we can see the pole at s = 1 + j0, and trivial as well as nontrivial zeroes; the vertical axis shows the magnitude of the output and the color codes the phase angle. Thank you very much beforehand.

[RameezRaja-qcfi]

Please make more videos of coding on heat transfer and fluid mechanics. Thank you very much!

[nickbe]

in line 52 (5:49) it says "IndentationError: unexpected indent" after having copied and pasted the code from your github

[hakankosebas]

could you do code of "Tutorial: How to simulate the wave equation" video by Nils Berglung