porous_medium_exact

porous_medium_exact, a MATLAB code which returns an exact solution of the porous medium equation (PME), dudt=Del^2(u^m), a partial differential equation (PDE) related to the diffusion equation, based on the Barenblatt solution.

Licensing:

The information on this web page is distributed under the MIT license.

Languages:

porous_medium_exact is available in a C version and a C++ version and a Fortran90 version and a MATLAB version and an Octave version and a Python version.

Related Data and codes:

porous_medium_exact_test

matlab_exact, a MATLAB code which evaluates exact solutions to a few selected examples of ordinary differential equations (ODE) and partial differential equations (PDE).

References:

1. Grigory Barenblatt,
   On some unsteady fluid and gas motions in a porous medium,
   Prikladnaya Matematika i Mekhanika (Applied Mathematics and Mechanics,
   Volume 16, Number 1, pages 67-78, 1952.
2. Rouben Rostamian,
   Programming Projects in C for Students of Engineering, Science, and Mathematics,
   SIAM, 2014,
   ISBN: 978-1-611973-49-5

Source Code:

• porous_medium_exact.m, returns an exact solution of the porous medium PDE.
• porous_medium_parameters.m, returns parameters of the porous medium PDE.
• porous_medium_residual.m, returns the residual of the porous medium PDE.