etdrk4

etdrk4, a MATLAB code which uses the ETD RK4 method to solve systems 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:

etdrk4 is available in a FORTRAN90 version and a MATLAB version.

Related Data and Programs:

etdrk4_test

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

Author:

Aly-Khan Kassam, Lloyd Trefethen; Modifications 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:

• allencahn_etdrk4.m, solves the Allen-Cahn equation using the ETDRK4 method.
• allencahn_euler.m, solves the Allen-Cahn equation using the Euler method.
• burgers_etdrk4.m, solves the Burgers equation using the ETDRK4 method.
• c8mat_print.m, prints a C8MAT.
• c8mat_print_some.m, prints some of a C8MAT.
• c8vec_print_part.m, prints part of a C8VEC.
• cheb.m, returns a Chebyshev grid and differentiation matrix.
• kdv_etdrk4.m, solves the Korteweg-deVries equation using the ETDRK4 method.
• kursiv_etdrk4.m, solves the Kuramoto-Sivashinksy equation using the ETDRK4 method.
• r8mat_print.m, prints an R8MAT;
• r8mat_print_some.m, prints some of an R8MAT;
• r8vec_print.m, prints an R8VEC;