VisualPDE is a website designed to bring the world of partial differential equations to a wider audience through the use of real-time interactive web-based simulations usable on almost any device.

We provide numerous examples of such simulations exploring a wide variety of topics from waves and transport theory, to chaotic nonlinear physical systems and pattern-forming models in mathematical biology.

A good place to start is the library of examples of basic PDEs. Beyond specific examples, we hope to encourage advanced users to design their own examples, and share all of our website and simulation code freely under an MIT licence. Anyone can design their own model simulations, and share these with a URL, or copy the markdown-based website design hosted on GitHub to design their own website for use in teaching or research communication.

The ideas for this website originated in a Durham Centre for Academic Development collaborative innovation grant titled Accessible interactive visualisations in mathematical biology, which supported Alex Chudasama (a final-year undergraduate at Durham University) to design an early version of an interactive PDE solver based on this Gray–Scott reaction–diffusion simulator.

The current website and tools are written and maintained by Benjamin Walker, Adam Townsend and Andrew Krause. A more discursive preprint about the context, design, and applications of VisualPDE can be found here.