**flame_ode_test**,
a MATLAB program which
calls flame_ode() to consider an ordinary differential equation (ODE) which models
the growth of a ball of flame in a combustion process.

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

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

- flame_ode_test.m, calls all the tests.
- flame_ode_test.sh, runs all the tests.
- flame_ode_test.txt, the output file.

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

- base_run.m, the source code.
- base_run.txt, the output file.
- base_run.png, a plot of 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.

- uniform_run.m, the source code.
- uniform_run_output.txt, the output file.
- uniform_run.png, a plot of the solutions.
- uniform_qoi.png, a plot of the quantity of interest 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.

- qoi_quad.m, the source code.
- qoi_quad_output.txt, the output file.
- clenshaw_curtis_compute.m, a function which computes points and weights of a Clenshaw Curtis quadrature rule.