spiral_pde, an Octave 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.
Because of the large number of variables, ode45() might not be a suitable solver, since it can run out of memory. For this problem, a simple Forward Euler ODE approach is used instead.
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.
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