Allen Cahn Equation#

Module for defining the Allen-Cahn equation.

class AllenCahnEquation(alpha, beta)[source]#

Bases: Equation

Implementation of the N-dimensional Allen-Cahn equation, defined as follows:

\[\frac{\partial u}{\partial t} - \alpha \Delta u + \beta(u^3 - u) = 0\]

Here, \(\alpha\) and \(\beta\) are parameters of the equation.

Initialization of the AllenCahnEquation class.

Parameters:

  • alpha (float | int) – The diffusion coefficient.

  • beta (float | int) – The reaction coefficient.