# Generated ODE system for the Brusselator Equation

Here's the generated system of equations for the Brusselator, with dx = dy = 1/4

## Equations for u

[Differential(t)(u[2, 2](t)) ~ 1.0 + 160.0u[3, 2](t) + 160.0u[5, 2](t) - 320.0u[2, 2](t) + 160.0u[2, 3](t) + 160.0u[2, 5](t) - 320.0u[2, 2](t) + (u[2, 2](t)^2)*v[2, 2](t) - 4.4u[2, 2](t),
Differential(t)(u[3, 2](t)) ~ 1.0 + 160.0u[2, 2](t) + 160.0u[4, 2](t) - 320.0u[3, 2](t) + 160.0u[3, 3](t) + 160.0u[3, 5](t) - 320.0u[3, 2](t) + (u[3, 2](t)^2)*v[3, 2](t) - 4.4u[3, 2](t),
Differential(t)(u[4, 2](t)) ~ 1.0 + 160.0u[4, 3](t) + 160.0u[4, 5](t) - 320.0u[4, 2](t) + 160.0u[3, 2](t) + 160.0u[5, 2](t) - 320.0u[4, 2](t) + (u[4, 2](t)^2)*v[4, 2](t) - 4.4u[4, 2](t),
Differential(t)(u[5, 2](t)) ~ 1.0 + 160.0u[2, 2](t) + 160.0u[4, 2](t) - 320.0u[5, 2](t) + 160.0u[5, 3](t) + 160.0u[5, 5](t) - 320.0u[5, 2](t) + (u[5, 2](t)^2)*v[5, 2](t) - 4.4u[5, 2](t),
Differential(t)(u[2, 3](t)) ~ 1.0 + 160.0u[2, 2](t) + 160.0u[2, 4](t) - 320.0u[2, 3](t) + 160.0u[3, 3](t) + 160.0u[5, 3](t) - 320.0u[2, 3](t) + (u[2, 3](t)^2)*v[2, 3](t) - 4.4u[2, 3](t),
Differential(t)(u[3, 3](t)) ~ 1.0 + 160.0u[2, 3](t) + 160.0u[4, 3](t) - 320.0u[3, 3](t) + 160.0u[3, 2](t) + 160.0u[3, 4](t) - 320.0u[3, 3](t) + (u[3, 3](t)^2)*v[3, 3](t) - 4.4u[3, 3](t),
Differential(t)(u[4, 3](t)) ~ 1.0 + 160.0u[3, 3](t) + 160.0u[5, 3](t) - 320.0u[4, 3](t) + 160.0u[4, 2](t) + 160.0u[4, 4](t) - 320.0u[4, 3](t) + (u[4, 3](t)^2)*v[4, 3](t) - 4.4u[4, 3](t),
Differential(t)(u[5, 3](t)) ~ 1.0 + 160.0u[2, 3](t) + 160.0u[4, 3](t) - 320.0u[5, 3](t) + 160.0u[5, 2](t) + 160.0u[5, 4](t) - 320.0u[5, 3](t) + (u[5, 3](t)^2)*v[5, 3](t) - 4.4u[5, 3](t),
Differential(t)(u[2, 4](t)) ~ 1.0 + 160.0u[3, 4](t) + 160.0u[5, 4](t) - 320.0u[2, 4](t) + 160.0u[2, 3](t) + 160.0u[2, 5](t) - 320.0u[2, 4](t) + (u[2, 4](t)^2)*v[2, 4](t) - 4.4u[2, 4](t),
Differential(t)(u[3, 4](t)) ~ 1.0 + 160.0u[2, 4](t) + 160.0u[4, 4](t) - 320.0u[3, 4](t) + 160.0u[3, 3](t) + 160.0u[3, 5](t) - 320.0u[3, 4](t) + (u[3, 4](t)^2)*v[3, 4](t) - 4.4u[3, 4](t),
Differential(t)(u[4, 4](t)) ~ 1.0 + 160.0u[4, 3](t) + 160.0u[4, 5](t) - 320.0u[4, 4](t) + 160.0u[3, 4](t) + 160.0u[5, 4](t) - 320.0u[4, 4](t) + (u[4, 4](t)^2)*v[4, 4](t) - 4.4u[4, 4](t),
Differential(t)(u[5, 4](t)) ~ 1.0 + 160.0u[2, 4](t) + 160.0u[4, 4](t) - 320.0u[5, 4](t) + 160.0u[5, 3](t) + 160.0u[5, 5](t) - 320.0u[5, 4](t) + (u[5, 4](t)^2)*v[5, 4](t) - 4.4u[5, 4](t),
Differential(t)(u[2, 5](t)) ~ 1.0 + 160.0u[2, 2](t) + 160.0u[2, 4](t) - 320.0u[2, 5](t) + 160.0u[3, 5](t) + 160.0u[5, 5](t) - 320.0u[2, 5](t) + (u[2, 5](t)^2)*v[2, 5](t) - 4.4u[2, 5](t),
Differential(t)(u[3, 5](t)) ~ 1.0 + 160.0u[2, 5](t) + 160.0u[4, 5](t) - 320.0u[3, 5](t) + 160.0u[3, 2](t) + 160.0u[3, 4](t) - 320.0u[3, 5](t) + (u[3, 5](t)^2)*v[3, 5](t) - 4.4u[3, 5](t),
Differential(t)(u[4, 5](t)) ~ 1.0 + 160.0u[3, 5](t) + 160.0u[5, 5](t) - 320.0u[4, 5](t) + 160.0u[4, 2](t) + 160.0u[4, 4](t) - 320.0u[4, 5](t) + (u[4, 5](t)^2)*v[4, 5](t) - 4.4u[4, 5](t),
Differential(t)(u[5, 5](t)) ~ 1.0 + 160.0u[2, 5](t) + 160.0u[4, 5](t) - 320.0u[5, 5](t) + 160.0u[5, 2](t) + 160.0u[5, 4](t) - 320.0u[5, 5](t) + (u[5, 5](t)^2)*v[5, 5](t) - 4.4u[5, 5](t)] 

## Equations for v

[Differential(t)(v[2, 2](t)) ~ 160.0v[2, 3](t) + 160.0v[2, 5](t) - 320.0v[2, 2](t) + 160.0v[3, 2](t) + 160.0v[5, 2](t) - 320.0v[2, 2](t) + 3.4u[2, 2](t) - (u[2, 2](t)^2)*v[2, 2](t),
Differential(t)(v[3, 2](t)) ~ 160.0v[2, 2](t) + 160.0v[4, 2](t) - 320.0v[3, 2](t) + 160.0v[3, 3](t) + 160.0v[3, 5](t) - 320.0v[3, 2](t) + 3.4u[3, 2](t) - (u[3, 2](t)^2)*v[3, 2](t),
Differential(t)(v[4, 2](t)) ~ 160.0v[3, 2](t) + 160.0v[5, 2](t) - 320.0v[4, 2](t) + 160.0v[4, 3](t) + 160.0v[4, 5](t) - 320.0v[4, 2](t) + 3.4u[4, 2](t) - (u[4, 2](t)^2)*v[4, 2](t),
Differential(t)(v[5, 2](t)) ~ 160.0v[5, 3](t) + 160.0v[5, 5](t) - 320.0v[5, 2](t) + 160.0v[2, 2](t) + 160.0v[4, 2](t) - 320.0v[5, 2](t) + 3.4u[5, 2](t) - (u[5, 2](t)^2)*v[5, 2](t),
Differential(t)(v[2, 3](t)) ~ 160.0v[2, 2](t) + 160.0v[2, 4](t) - 320.0v[2, 3](t) + 160.0v[3, 3](t) + 160.0v[5, 3](t) - 320.0v[2, 3](t) + 3.4u[2, 3](t) - (u[2, 3](t)^2)*v[2, 3](t),
Differential(t)(v[3, 3](t)) ~ 160.0v[3, 2](t) + 160.0v[3, 4](t) - 320.0v[3, 3](t) + 160.0v[2, 3](t) + 160.0v[4, 3](t) - 320.0v[3, 3](t) + 3.4u[3, 3](t) - (u[3, 3](t)^2)*v[3, 3](t),
Differential(t)(v[4, 3](t)) ~ 160.0v[3, 3](t) + 160.0v[5, 3](t) - 320.0v[4, 3](t) + 160.0v[4, 2](t) + 160.0v[4, 4](t) - 320.0v[4, 3](t) + 3.4u[4, 3](t) - (u[4, 3](t)^2)*v[4, 3](t),
Differential(t)(v[5, 3](t)) ~ 160.0v[2, 3](t) + 160.0v[4, 3](t) - 320.0v[5, 3](t) + 160.0v[5, 2](t) + 160.0v[5, 4](t) - 320.0v[5, 3](t) + 3.4u[5, 3](t) - (u[5, 3](t)^2)*v[5, 3](t),
Differential(t)(v[2, 4](t)) ~ 160.0v[2, 3](t) + 160.0v[2, 5](t) - 320.0v[2, 4](t) + 160.0v[3, 4](t) + 160.0v[5, 4](t) - 320.0v[2, 4](t) + 3.4u[2, 4](t) - (u[2, 4](t)^2)*v[2, 4](t),
Differential(t)(v[3, 4](t)) ~ 160.0v[2, 4](t) + 160.0v[4, 4](t) - 320.0v[3, 4](t) + 160.0v[3, 3](t) + 160.0v[3, 5](t) - 320.0v[3, 4](t) + 3.4u[3, 4](t) - (u[3, 4](t)^2)*v[3, 4](t),
Differential(t)(v[4, 4](t)) ~ 160.0v[3, 4](t) + 160.0v[5, 4](t) - 320.0v[4, 4](t) + 160.0v[4, 3](t) + 160.0v[4, 5](t) - 320.0v[4, 4](t) + 3.4u[4, 4](t) - (u[4, 4](t)^2)*v[4, 4](t),
Differential(t)(v[5, 4](t)) ~ 160.0v[2, 4](t) + 160.0v[4, 4](t) - 320.0v[5, 4](t) + 160.0v[5, 3](t) + 160.0v[5, 5](t) - 320.0v[5, 4](t) + 3.4u[5, 4](t) - (u[5, 4](t)^2)*v[5, 4](t),
Differential(t)(v[2, 5](t)) ~ 160.0v[2, 2](t) + 160.0v[2, 4](t) - 320.0v[2, 5](t) + 160.0v[3, 5](t) + 160.0v[5, 5](t) - 320.0v[2, 5](t) + 3.4u[2, 5](t) - (u[2, 5](t)^2)*v[2, 5](t),
Differential(t)(v[3, 5](t)) ~ 160.0v[2, 5](t) + 160.0v[4, 5](t) - 320.0v[3, 5](t) + 160.0v[3, 2](t) + 160.0v[3, 4](t) - 320.0v[3, 5](t) + 3.4u[3, 5](t) - (u[3, 5](t)^2)*v[3, 5](t),
Differential(t)(v[4, 5](t)) ~ 160.0v[4, 2](t) + 160.0v[4, 4](t) - 320.0v[4, 5](t) + 160.0v[3, 5](t) + 160.0v[5, 5](t) - 320.0v[4, 5](t) + 3.4u[4, 5](t) - (u[4, 5](t)^2)*v[4, 5](t),
Differential(t)(v[5, 5](t)) ~ 160.0v[2, 5](t) + 160.0v[4, 5](t) - 320.0v[5, 5](t) + 160.0v[5, 2](t) + 160.0v[5, 4](t) - 320.0v[5, 5](t) + 3.4u[5, 5](t) - (u[5, 5](t)^2)*v[5, 5](t)]

## Boundary condition Equations

u[2, 1](t) ~ u[2, 5](t),
u[3, 1](t) ~ u[3, 5](t),
u[4, 1](t) ~ u[4, 5](t),
u[5, 1](t) ~ u[5, 5](t),
u[1, 2](t) ~ u[5, 2](t),
u[1, 3](t) ~ u[5, 3](t),
u[1, 4](t) ~ u[5, 4](t),
u[1, 5](t) ~ u[5, 5](t),
u[1, 1](t) ~ 0, # Invalid corner point set to 0
v[2, 1](t) ~ v[2, 5](t),
v[3, 1](t) ~ v[3, 5](t),
v[4, 1](t) ~ v[4, 5](t),
v[5, 1](t) ~ v[5, 5](t),
v[1, 2](t) ~ v[5, 2](t),
v[1, 3](t) ~ v[5, 3](t),
v[1, 4](t) ~ v[5, 4](t),
v[1, 5](t) ~ v[5, 5](t),
v[1, 1](t) ~ 0] # Invalid corner point set to 0

On the call to ODEProblem, this code is generated.