# spiral_pde

spiral_pde, 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.

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
```

### Languages:

spiral_pde 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 05 February 2021.