Heat Equation

A simulation and visual representation of the 2nd order differential “heat equation”.

The equation is defined as :

I made this for a Calculus BC project and modeled the equation pretty simply with Javascript.

Basically, a grid of NxN cells are created and each cell has a couple of properties:
Current temperature, u,
Thermal diffusivity, a,
and its position in (2D) space, x, y.

Then, each ‘step’ of the simulation in time, changes each cell’s temperature by an amount modeled by the equation multiplied by the magnitude of the step in time ‘dt’.

You can play around with it here:

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