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So I have implemented central finite difference method for solving the 2D heat equation. When I leave all initial and boundary conditions as 0s, but apply an input uniform across the entire space or grid, I am only noticing temperature response at the boundary. I am not sure exactly what is causing this.

The code is here: https://colab.research.google.com/drive/1YCh_DDrw0uZPLvrWKU2hcw6lSe7cQiRS

But for a quick example of what this looks like:

enter image description here

Would really appreciate any help with looking at the code to see what's causing this. Is there any chance that my algorithm is unstable and I need to increase the discretization points or something?

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    $\begingroup$ I expect nobody is going to help, because your code requires asking for access. $\endgroup$
    – Joscha Fregin
    Commented Jan 26, 2023 at 13:13
  • $\begingroup$ @JoschaFregin I just edited the access permission to anyone with the link $\endgroup$
    – pythonengineer
    Commented Jan 26, 2023 at 15:38
  • $\begingroup$ In your code's odefunc function, you take T as an argument and then promptly set it ot the zero matrix. That's likely not what you intended. $\endgroup$
    – Wolfgang Bangerth
    Commented Jan 26, 2023 at 16:50
  • $\begingroup$ Okay, I corrected this, I also set the initial dTdt to be empty instead of zeros as well. This should be fine, correct? I am still seeing a weird plot now however if you look back at the code. It looks like maybe some of the ODE solutions for some of the points are diverging? $\endgroup$
    – pythonengineer
    Commented Jan 26, 2023 at 16:59

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