This repository contains the Jupyter notebooks written in Python that illustrate applications of PDEs:
- Bacteria model: dynamics of nonlinear diffusion equations with logistic nonlinearities on bounded intervals with Neumann boundary conditions
- Brusselator: stripes and spots that arise via Turing bifurcations in the planar Brusselator model of an autocatalytic chemical reaction (nonlinear diffusion equation on the square with periodic boundary conditions)
- Korteweg-de Vries: explores the dynamics of solitons and their interactions in the nonlinear KdV equation with periodic boundary conditions
- Navier-Stokes: illustrates fluid flow in a planar box with moving lid (adapted from code by Barba group)
- SIR model: explores the spreading of infectious diseases in space in a nonlinear heat equation with SIR nonlinearity
- Stochastic population model: compares the dynamics of the logistic ODE with multiplicative noise to the stationary solution of the associated Fokker-Planck equation
- Stochastic wealth distribution model: compares the dynamics of a stochastic ODE model for the distribution of wealth with stationary solutions of the associated Fokker-Planck equations, and illustrates Pareto indices
If you would like to run these notebooks in your webbrowser using Binder, click on the badge below. It may take time for Binder to start, and the notebooks may also run significantly slower than when ran locally.
Alternatively, install a JupyterLab with a Python 3 kernel locally using, for instance, Anaconda. If the command %matplotlib widget results in an error, replace it with %matplotlib notebook.
