# ‘py-pde’ python package

The py-pde python package provides methods and classes useful for solving partial differential equations (PDEs) of the form

$\partial_t u(\boldsymbol x, t) = \mathcal D[u(\boldsymbol x, t)] + \eta(u, \boldsymbol x, t) \;,$

where $$\mathcal D$$ is a (non-linear) differential operator that defines the time evolution of a (set of) physical fields $$u$$ with possibly tensorial character, which depend on spatial coordinates $$\boldsymbol x$$ and time $$t$$. The framework also supports stochastic differential equations in the Itô representation, where the noise is represented by $$\eta$$ above.

The main audience for the package are researchers and students who want to investigate the behavior of a PDE and get an intuitive understanding of the role of the different terms and the boundary conditions. To support this, py-pde evaluates PDEs using the methods of lines with a finite-difference approximation of the differential operators. Consequently, the mathematical operator $$\mathcal D$$ can be naturally translated to a function evaluating the evolution rate of the PDE.

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