Heat & Wave Fields
Two of the most important PDEs in physics, solved live: diffuse heat across a 2D plate, or send waves down a string. Interact directly with the field.
Field — 2D Heat EquationLive
explicit finite difference · ∂u/∂t = α∇²u
Controls
Data Inspector
Grid120×120
SchemeExplicit FD
Stabilitystable
Governing equation
Reading this result: Diffusivity α = 0.20 spreads heat at a moderate rate while staying well under the 0.25 explicit-stability limit — hotspots smooth into a gentle gradient within a second or two.
Runs locally in your browser — free forever. Scale to the cloud when reality gets heavy.
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How it works
The heat equation is solved with an explicit finite-difference scheme on a 2D grid, stable while the diffusivity stays within the CFL limit. The wave equation uses a second-order-in-time explicit stencil with light damping. Both run entirely on your device — click to inject heat or pluck the string and watch the PDE respond.
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Frequently asked questions
Is this PDE simulation tool really free?▾
Yes. Heat & Wave Fields runs entirely in your browser using your device's own compute, so local use is free forever. You only pay Compute Tokens if you scale a job to the cloud.
Do I need to install anything?▾
No. Everything runs client-side in a modern browser — no downloads, no license, no account required to start.
Can I save or share my simulation?▾
Create a free account to save projects, and use a shareable embed or minted DOI to publish a live, interactive version anywhere.
How accurate are the results?▾
The solver uses established numerical methods, but results are for research and educational purposes and should be validated against experiment or professional review before you rely on them.