spiral_pde_movie, a MATLAB 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. The sequence of solutions is bundled into a movie.
The equations to be solved approximately involve the Laplacian operator. The user has a choice of several functions that can estimate this value. The version using a 5 point stencil produces spiral solutions that are somewhat square in shape, while the 9 point stencil produces a rounder and more symmetric spiral.
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
Here is an image of the pair of solutions at time t=5:
The computer code and data files described and made available on this web page are distributed under the MIT license
spiral_pde_movie is available in a MATLAB version.
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