The py-pde python package provides methods and classes useful for solving partial differential equations (PDEs) of the form
∂tu(x, t) = 𝒟[u(x, t)] + η(u, x, t) ,
where 𝒟 is a (non-linear) operator containing spatial derivatives that defines the time evolution of a (set of) physical fields u with possibly tensorial character, which depend on spatial coordinates x and time t. The framework also supports stochastic differential equations in the Itô representation, where the noise is represented by η 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 𝒟 can be naturally translated to a function evaluating the evolution rate of the PDE.
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