Note
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2.6. Kuramoto-Sivashinsky - Using PDE class
This example implements a scalar PDE using the PDE
. We here
consider the Kuramoto–Sivashinsky equation, which for instance
describes the dynamics of flame fronts:
\[\partial_t u = -\frac12 |\nabla u|^2 - \nabla^2 u - \nabla^4 u\]

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from pde import PDE, ScalarField, UnitGrid
grid = UnitGrid([32, 32]) # generate grid
state = ScalarField.random_uniform(grid) # generate initial condition
eq = PDE({"u": "-gradient_squared(u) / 2 - laplace(u + laplace(u))"}) # define the pde
result = eq.solve(state, t_range=10, dt=0.01)
result.plot()
Total running time of the script: (0 minutes 28.160 seconds)