‘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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