spiral_pde, a Python code which solves a pair of reaction-diffusion partial differential equations (PDE), in two spatial dimensions and time, over a rectangular domain with periodic boundary condition, whose solution is known to evolve into a pair of spirals.
A simple Forward Euler ODE approach is used to solve the differential equations.
The PDE has the form:
du/dt = del u + u * ( 1 - u ) * ( u - ( v + beta ) / alpha ) ) / epsilon
dv/dt = delta * del v + u - v
The domain is the square 0 <= x <= 80, 0 <= y <= 80, with zero Neumann boundary conditions.
The initial conditions are
u = 0 for x < 40
1 for 40 < x
v = 0 for y < 40
alpha/2 for 40 < y
The parameters are
alpha = 0.25
beta = 0.001
delta = 0.0
epsilon = 0.002
The information on this web page is distributed under the MIT license.
spiral_pde is available in a MATLAB version and an Octave version and a Python version.
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.
gray_scott_pde, a Python code which solves the partial differential equation (PDE) known as the Gray-Scott reaction diffusion equation, displaying a sequence of solutions as time progresses.
wave_pde, a Python code which uses the finite difference method (FDM) in space, and the method of lines in time, to set up and solve the partial differential equations (PDE) known as the wave equations, utt = c uxx, in one spatial dimension and time.
Plots were made every 500 steps.
