allen_cahn_pde


allen_cahn_pde, a Python 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 information on this web page is 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:

diffusion_pde, a Python code which solves the diffusion partial differential equation (PDE) dudt - mu * d2udx2 = 0 in one spatial dimension, with a constant diffusion coefficient mu, and periodic boundary conditions, using FTCS, the forward time difference, centered space difference method.

gray_scott_pde, a Python code which solves the partial differential equation (PDE) known as the Gray-Scott reaction diffusion equation, in two spatal dimension and time, displaying a sequence of solutions as time progresses.

spiral_pde, a Python code which solves a pair of reaction-diffusion partial differential equations (PDE) over a rectangular domain with periodic boundary condition, whose solution is known to evolve into a pair of spirals.

wave_pde, a Python code which uses the finite difference method (FDM) in space, and the method of lines in time, to set up and solve the partial differential equations (PDE) known as the wave equations, utt = c uxx, in one spatial dimension and time.

Reference:

  1. Costica Morosanu, Silvio Paval,
    On the numerical approximation of a nonlinear reaction-diffusion equation with non-homogeneous Neumann boundary conditions. Case 1D,
    Submitted.
  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:


Last revised on 10 November 2020.