HeatEquation-JS 🔥

In mathematics, if given an open subset $U$ of ${\mathbb{R}}^2$ and a subinterval $I$ of $\mathbb{R}$, one says that a function $u:U\times I\to \mathbb{R}$ is a solution of the heat equation if

$$\frac{\partial u}{\partial t}=\alpha \mathrm{\Delta }u$$

Where $\mathrm{\Delta }u$ is the Laplacian of the function $u$

$$\mathrm{\Delta }u=\sum _{i=1}^n\frac{{\partial }^{2}u}{\partial x_i^2}=\frac{{\partial }^{2}u}{\partial x^2}+\frac{{\partial }^{2}u}{\partial y^2}$$

where $(x,y;t)$ denotes a general point of the domain. It is typical to refer to $t$ as "time" and $x$, $y$ as "spatial variables," even in abstract contexts where these phrases fail to have their intuitive meaning. For any given value of $t$, the right-hand side of the equation is the Laplacian of the function $u(x,y;t):U\to \mathbb{R}$

$\alpha$ is the diffusivity constant

Demo

Simulation

Dependencies

p5.js for drawing