flame_ode

flame_ode, a Python code which considers an ordinary differential equation (ODE) which models the growth of a ball of flame in a combustion process. The exact solution is defined in terms of the Lambert W function.

Licensing:

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

Languages:

flame_ode is available in a MATLAB version and an Octave version and a Python version.

Related Data and codes:

flame_exact, a Python code which returns the exact solution of an ordinary differential equation (ODE) which models the growth of a ball of flame in a combustion process. The exact solution is defined in terms of the Lambert W function.

flame_odefun, a Python code which uses odefun() from the multiple precision package mpmath() to solve an ordinary differential equation (ODE) which models the growth of a ball of flame in a combustion process.

python_ode, Python codes which sets up various systems of ordinary differential equations (ODE).

References:

1. Shirley Abelman, Kailash Patidar,
   Comparison of some recent numerical methods for initial-value problems for stiff ordinary differential equations,
   Computers and Mathematics with Applications,
   Volume 55, Number 4, 2008, pages 733-744.
2. Guy Rouleau,
   Guy on Simulink: Why do we need stiff ODE solvers?,
   "https://blogs.mathworks.com/simulink/2012/07/03/why-do-we-need-stiff-ode-solvers/?s_tid=srchtitle",
   Posted 03 July 2012.
3. Cleve Moler,
   Cleve's Corner: Stiff Differential Equations,
   MATLAB News and Notes,
   May 2003, pages 12-13.
4. Cleve Moler,
   Cleve's Corner: Ordinary Differential Equations, Stiffness,
   "https://blogs.mathworks.com/cleve/2014/06/09/ordinary-differential-equations-stiffness/?s_tid=srchtitle",
   Posted 09 June 2014.

Source Code:

• flame_ode.py, the source code.
• flame_ode.sh, runs all the tests.
• flame_ode.txt, the output file.

• flame_euler.png, a plot of the solution, for delta = 0.01;
• flame_solve_ivp.png, a plot of the solution, for delta = 0.01;