This might be the subject of the next video, Thank you for you suggestion!

Using a pre built library/code will render a math video useless. I, like many others, have come here to learn math not a fancy python library. Good work younes!

No need for the cheeky answer, I was just trying to mention the info for people who are more interested in the performance aspect and are maybe looking for such implementations. @@jawadmansoor2456

Could you recommend a video that uses that library please?

@@ssrini2002 I couldn't find any videos actually, there are a couple of websites with code examples, just google "python diffusion sparse matrix" and you'll find them quickly. Although, seeing as there's no videos about this, I might make one myself :)

Thank you for your comment @vikinja121 and for the clarification

I will be sure to make these in the future, thank you for your feedback!

Thank you for your feedback ^^ Personally I am not that familiar with cuda (though this surely is motivating me to make a video about it 🤔) However there are several techniques you can use drastically improuve the speed (method I discoreved after making the video) * writing the main calculations as a function, then using numba's jit to optimize the computation (by chacing it, ...) * Important note: since the result of each iteration is more or less dependent on the one before, parallezing will most likely not work, however one trick you can use is to vectorize the code by, instead of writing it in form of a loop, you replace it by some sort of linear system of equations A*T = b, which will be way faster since it uses linear algebra to find the solution (using numpy)

Hello! We use a separate copy of the array `u` because it represents the temperature distribution at a specific time, `t`. When we discretize our equation in time and space, we get: u[t+1, i] = (dt * a / dx^2) * (u[t, i-1] - 2 * u[t, i] + u[t, i+1]) + u[t, i] In this equation, `u[t, ...]` represents the temperature distribution at time `t`. By updating `u` using a while loop, we ensure that the computation of the distribution at all nodes is accurate for time `t`. If we don't use a copy of `u`, we end up computing the solution at `t+1` using a mixture of data from both `t` and `t+1`. For example, without a copy, `u` is updated dynamically, and when computing each node [i], the left node [i-1] is used from time `t+1` while the right node [i+1] is still from time `t`. This leads to: u[t+1, i] = (dt * a / dx^2) * (u[t+1, i-1] - 2 * u[t, i] + u[t, i+1]) + u[t, i] This does not conform to the established numerical scheme. I hope this clarifies why it's necessary to use a copy of the array `u` in the scheme equation. Let me know if you have any other questions! :)

The formulas represent an approximation of derivative via a method called "the finite difference method" often called FDM, this method represent a simple but powerfull technique for solving differential equation related problems (especially flow/heat problems) If you want to learn more about it I suggest you to watch another video I made (part 1) kzfaq.info/get/bejne/kNuodL2pzNvaXWQ.html

Thank you for your Comment. Very Interesting function and Idea, I will look forward into making it.

If you are getting an "IndentationError: unexpected indent" this means there is a problem with the indentation (tabbing) of the line, make sure to delete the tabs and manually re do it.

Great suggestion thank you ^^' ! I will plan on doing this video about the wave equation it will be an interessting subject (in a couple of weeks)

@@YounesLab thanks

If you mean for making the simulation i only used Visual Studio Code (for python IDLE)