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.
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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.
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.