allen_cahn_pde_etdrk4

allen_cahn_pde_etdrk4, a MATLAB code which uses the exponential time differencing (ETD) RK4 method to solve the Allen-Cahn system of stiff ordinary differential equations (ODE), by Aly-Khan Kassam, Lloyd Trefethen.

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_etdrk4 is available in a MATLAB version.

Related Data and Programs:

allen_cahn_pde_etdrk4_test

kdv_etdrk4, a MATLAB code which uses the ETDRK4 method to solve the Korteweg-DeVries equation, by Aly-Khan Kassam, Lloyd Trefethen.

kdv_ift, a MATLAB code which uses the IFT method to solve the Korteweg-DeVries equation, by Aly-Khan Kassam, Lloyd Trefethen.

Author:

Original MATLAB version by Aly-Khan Kassam, Lloyd Trefethen; This version by John Burkardt.

Reference:

1. Stephen Cox, Paul Matthews,
   Exponential time differencing for stiff systems,
   Journal of Computational Physics,
   Volume 176, pages 430-455, 2002.
2. Aly-Khan Kassam, Lloyd Trefethen,
   Fourth-order time-stepping for stiff ODE's,
   SIAM Journal on Scientific Computing,
   Volume 26, Number 4, pages 1214-1233, 2005.
3. Lloyd Trefethen,
   Spectral methods in MATLAB,
   SIAM, 2000,
   LC: QA377.T65
   ISBN: 978-0-898714-65-4

Source Code:

• allen_cahn_pde_etdrk4.m, solves the Allen-Cahn equation using the ETDRK4 method.
• cheb.m, returns a Chebyshev grid and differentiation matrix.