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Thank you!! It's all thanks to the quality feedback I am getting from all of you! 😄

Thank you I am glad to hear it Sharing Knowledge is honorable, I encourage you to continue doing it! 👏 And all the best in your video making ^^

I appreciate it! Thank you I did somewhat of a simple 3d animation with the lorenz attractor you can check it out: th-cam.com/video/GdNjTJZnTmM/w-d-xo.html&ab_channel=YounesLab And I am currently working on the 3 body problem so be sure to stick around!

That true thank you for letting me knoy, I will fix it in the Git-Hub code. If we have `n` interval we always have `n+1` nodes. When considering the simple example of a 1 meter long rod with two nodes, lenght = 1, and dx = 1 meaning nodes = lenght//dx + 1

True, 'axis' refers to a single object, where 'axes' refer to multiple ones within one figure. Thank you for pointing this one out! :)

This might be happening in a near future hopefully 😁

@@YounesLab will it be a separate course or integrated modules within an existing course?

It will likely be a seperate course. However, I might include a small recap (summary) and integrate a small portion as a module in my Python existing course (to give an overall tool kit for engineers) Being a seperate course, it will have some prerequisites such as a deep understanding of Python when it comes to computational physics, calculus, and so on. More about it soon! 😄

Thank you for your support 👏

21:32 time

Indeed! I made a little typo mistake there abd it should be x, y, and z. Thank you for for letting me know! I will correct it in the github as well

In order to update text within your animation, you have to set the blit mode to false `blit=False` and then specify within the update function a line that update the title for example: fig, axis = plt.subplots() animated_bridge, = axis.plot([], [], color='blue') # ',' is used because axis.plot returns an array axis.set_xlim([0, L]) axis.set_ylim([-10, 10]) axis.set_title(f"Frame: {0} / {len(time_points)}") # Initial title def update(frame): print(frame) animated_bridge.set_data(space_points, u[frame]) # Updating the data across [frame] axis.set_title(f"Frame: {frame} / {len(time_points)}") return animated_bridge

I am glad to hear it! :)

Ah, I see you're a man of culture as well. Thank you kind sir

This really is an underrated advice that people often overlook! Sleep really is the foundation of everything. There is a quote I heard once saying "sacrificing the night-life for the morning-life" meaning to improuve you have to be willing to give up on the (bad) night behavior 🤔 Thank you for sharing! :)

Pretty much 🤔 depending on how brave you are you can also do it with vegetables

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) th-cam.com/video/ZuxAZxguv-0/w-d-xo.html

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)

If you elaborate, I can have a look at 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

I very glad to hear your feedback and know it was helpful! ^^' I did make a video in the past about animating (simple animation) the mass-spring system if you checked it out already, where we can see the elongation of the spring (th-cam.com/video/nT16-yQrnFk/w-d-xo.html) Now for the real spring contraction and relaxation is an interessting topic I will through it! Thank you for your suggestion!

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! :)