FLAME_ODE
An Ordinary Differential Equation for Combustion

FLAME_ODE, a MATLAB library which considers an ordinary differential equation (ODE) which models the growth of a ball of flame in a combustion process.

Licensing:

The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.

Languages:

FLAME_ODE is available in a MATLAB version.

Related Data and Programs:

flame_ode_test

LORENZ_ODE, a MATLAB program which approximates solutions to the Lorenz system, creating output files that can be displayed by gnuplot.

PENDULUM_ODE, a MATLAB library which looks at some simple topics involving the linear and nonlinear ordinary differential equations (ODEs) that represent the behavior of a pendulum of length L under a gravitational force of strength G.

PREDATOR_PREY_ODE, a MATLAB program which solves a pair of predator prey ordinary differential equations (ODE's) using MATLAB's ode23() solver.

RKF45, a MATLAB library which implements the Runge-Kutta-Fehlberg ODE solver.

SPRING_ODE, a MATLAB program which shows how line printer graphics can be used to make a crude illustration of a solution of the ordinary differential equation (ODE) that describes the motion of a weight attached to a spring.

SPRING_ODE2, a MATLAB program which shows how gnuplot graphics can be used to illustrate a solution of the ordinary differential equation (ODE) that describes the motion of a weight attached to a spring.

TEST_ODE, a MATLAB library which defines ordinary differential equations (ODE) test problems.

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.
Cleve Moler,
Cleve's Corner: Stiff Differential Equations,
MATLAB News and Notes,
May 2003, pages 12-13.

Source Code:

FLAME_FUN is a function which defines the right hand side of the ODE, in a format required by MATLAB's ode45() function.

• flame_fun.m, code defining the right hand side of the ODE.
• event_function.m, code which can tell ODE45 to watch out for the time at which the solution achieves the value 0.99.
• timestamp.m, prints the YMDHMS date as a timestamp.