gray_scott_pde

gray_scott_pde, a Python code which solves the partial differential equation (PDE) known as the Gray-Scott reaction diffusion equation, in two spatial dimension and time, displaying a sequence of solutions as time progresses.

Licensing:

The information on this web page is distributed under the MIT license.

Languages:

gray_scott_pde is available in a MATLAB version and an Octave version and a Python version.

Related Data and Programs:

allen_cahn_pde, a Python code which sets up and solves the Allen-Cahn reaction-diffusion system of partial differential equations (PDE) in 1 space dimension and time.

diffusion_pde, a Python code which solves the diffusion partial differential equation (PDE) dudt - mu * d2udx2 = 0 in one spatial dimension, with a constant diffusion coefficient mu, and periodic boundary conditions, using FTCS, the forward time difference, centered space difference method.

spiral_pde, a Python code which solves a pair of reaction-diffusion partial differential equations (PDE) over a rectangular domain with periodic boundary condition, whose solution is known to evolve into a pair of spirals.

Reference:

• Willem Hundsdorfer, Jan Verwer,
  Numerical solution of time-dependent advection-diffusion-reaction equations,
  Springer, 2003,
  ISBN: 978-3-662-09017-6

Source Code:

• gray_scott_pde.py the source code.
• gray_scott_pde.sh runs all the tests.
• gray_scott_pde.txt the output file.

• gray_scott_u0000.png, U solution at time 0.
• gray_scott_u0100.png, U solution at time 100.
• gray_scott_u0200.png, U solution at time 200.
• gray_scott_u0500.png, U solution at time 500.
• gray_scott_u1000.png, U solution at time 1000.
• gray_scott_u1500.png, U solution at time 1500.