FLAME_ODE
An Ordinary Differential Equation for Combustion


FLAME_ODE is 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:

DFIELD8, a MATLAB program which interactively displays the direction field of a differential equation, by John Polking.

ODE_PREDATOR_PREY, a MATLAB program which solves a time-dependent predator-prey system using MATLAB's ODE23 solver.

PPLANE8, a MATLAB program which interactively displays the phase plane of a differential equation, by John Polking.

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.
  2. 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.

BASE_RUN solves the problem with DELTA=0.01, and plots the solution.

UNIFORM_RUN solves the problem multiple times, using a value of DELTA that is the product of the base value 0.01 times a factor whose logarithm base 2 varies uniformly between -1 and 1. The quantity of interest Q is the time at which the solution reaches the value 0.99. The program plots the solution curves, as well as the observed values of Q as a function of DELTA.

QOI_QUAD assumes that the actual value of DELTA can be written as DELTA = 2^U*DELTA_BASE, where DELTA_BASE is 0.01 and U is a number that is uniformly distributed in [-1,+1]. We now seek to estimate the expected value of the quantity of interest using a Clenshaw-Curtis quadrature rule to select values of U, compute the quantity of interest, and weight them.

You can go up one level to the MATLAB source codes.


Last revised on 18 February 2013.