allen_cahn_pde

allen_cahn_pde, a MATLAB code which sets up and solves the Allen-Cahn reaction-diffusion system of partial differential equations (PDE) in 1 space dimension and time.

Licensing:

The computer code and data files described and made available on this web page are distributed under the MIT license

Languages:

allen_cahn_pde is available in a MATLAB version and an Octave version and a Python version.

Related Data and Programs:

allen_cahn_pde_test

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Reference:

1. Costica Morosanu, Silvio Paval,
   On the numerical approximation of a nonlinear reaction-diffusion equation with non-homogeneous Neumann boundary conditions. Case 1D,
   ROMAI Journal, Volume 15, Number 2, pages 43-60, 2019.
2. Jian Zhang, Qiang Du,
   Numerical studies of discrete approximations to the Allen-Cahn equation in the sharp interface limit,
   SIAM Journal on Scientific Computing,
   Volume 31, Number 4, pages 3042-3063, 2009.

Source Code:

• allen_cahn_deriv.m, sets up the right hand side of the PDE.
• allen_cahn_initial_condition.m, sets an initial condition proposed by Morosanu and Paval.
• allen_cahn_parameters.m, returns parameters of the PDE.
• laplacian_interval.m, estimates the second derivative of a function of x whose values are given at equally spaced points.