porous_medium_exact, a Fortran 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.


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


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:


f90_exact, a Fortran90 code which evaluates exact solutions to a few selected examples of ordinary differential equations (ODE) and partial differential equations (PDE).


  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:

Last revised on 19 May 2024.