# spiral_pde_movie

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: ### Languages:

spiral_pde_movie is available in a MATLAB version.

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### Reference:

Willem Hundsdorfer, Jan Verwer,
Numerical solution of time dependent advection-diffusion-reaction equations,
Springer Series in Computational Mathematics,
Volume 33, Berlin, 2003.

### Source Code:

Last revised on 04 February 2021.